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1.

図書

図書
edited by Bernold Fiedler
出版情報: Amsterdam ; Tokyo : Elsevier Science, 2002-  3 v. ; 25 cm
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Principal structures / B. Hasselblatt ; A. KatokVolume 1A:
Entropy, Isomorphism and Equivalence / J.-P. Thouvenot
Hyperbolic dynamics
Invariant measures for hyperbolic dynamical systems / N. Chernov
Periodic orbits and zeta functions / M. Pollicott
Hyperbolic dynamics and Riemannian geometry / G. Knieper
Topological Methods in Dynamics / J. Franks ; M. Misiurewicz
One-Dimensional Maps / M. Jakobson ; G. Sawiatek
Ergodic theory and dynamics of G-spaces / R. Feres
Symbolic and algebraic dynamical systems / D. Lind ; K. Schmidt
Homogeneous flows, applications to number theory, and related topics / D. Kleinbock ; N. Shah ; A. Starkov
Random transformations in ergodic theory / A. Furman
Rational billiards and flat structures / H. Masur ; S. Tabachnikov
Variational methods for Hamiltonian systems / P.H. Rabinowitz
Pseudoholomorphic curves and dynamics in three dimensions / H. Hofer ; K. Wysocki ; E. Zehnder
Finite-Dimensional Methods / A:
Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators / N. Kopell ; G.B. Ermentrout1:
Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere / C. Jones ; S. Winkler2:
Geometric singular perturbation analysis of neuronal dynamics / J.E. Rubin ; D. Terman3:
Numerics / B:
Numerical continuation, and computation of normal forms / W.-J. Beyn ; A. Champneys ; E. Doedel ; W. Govaerts ; Y.A. Kuznetsov ; B. Sandstede4:
Set oriented numerical methods for dynamical systems / M. Dellnitz ; O. Junge5:
Numerics and exponential smallness / V. Gelfreich6:
Shadowability of chaotic dynamical systems / C. Grebogi ; L. Poon ; T. Sauer ; J.A. Yorke ; D. Auerbach7:
Numerical analysis of dynamical systems / J. Guckenheimer8:
Topological Methods / C:
Conley index / K. Mischaikow ; M. Mrozek9:
Functional differential equations / R.D. Nussbaum10:
Partial Differential Equations / D:
Navier--Stokes equations and dynamical systems / C. Bardos ; B. Nicolaenko11:
The nonlinear Schrodinger equation as both a PDE and a dynamical system / D. Cai ; D.W. McLaughlin ; K.T.R. McLaughlin12:
Pattern formation in gradient systems / P.C. Fife13:
Blow-up in nonlinear heat equations from the dynamical systems point of view / M. Fila ; H. Matano14:
The Ginzburg--Landau equation in its role as a modulation equation / A. Mielke15:
Parabolic equations: asymptotic behavior and dynamics on invariant manifolds / P. Polacik16:
Global attractors in partial differential equations / G. Raugel17:
Stability of travelling waves / 18:
Preface List of Contributors Contents of Volume 1A
Partially Hyperbolic Dynamical Systems / Ya. Pesin
Smooth Ergodic Theory and Nonuniformly Hypoerbolic Dynamics / L. Barreira
Appendix / O. Sarig
Stochastic-Like Behaviour in Nonuniformly Expanding Maps / S. Luzzatto
Homoclinic Bifurcations, Dominated Splitting, and Robust Transivity / E.R. Pujals ; M. Sambarino
Random Dynamics / Yu. Kifer ; P.-D. Liu
An Introduction to Veech Surfaces / P. Hubert ; T.A. Schmidt
Ergodic Theory of Translation Surfaces
On the Lyapunov Exponents of the Kontsevich-Zorich Cocycle / G. Forni
Counting Problems in Moduli Space / A. Eskin
On the Interplay Between Measurable and Topological Dynamics / E. Glasner ; B. Weiss
Spectral Properties and Combinatorial Constructions in Ergodic Theory
Combinatorial and Diophantine Applications of Ergodic Theory / V. Bergelson
Appendix A / A. Leibman
Appendix B / A. Quas ; M. Wierdl
Pointwise Ergodic Theorems for Actions of Groups / A. Nevo
Global Attractors in PDE / A.V. Babin
Hamiltonian PDEs / S.B. Kuksin
Extended Hamiltonian Systems / D. Bambusi ; M.I. Weinstein
Author Index of Volume 1A
Subject Index of Volume 1A
Author Index
Subject Index
Principal structures / B. Hasselblatt ; A. KatokVolume 1A:
Entropy, Isomorphism and Equivalence / J.-P. Thouvenot
Hyperbolic dynamics
2.

図書

図書
Michael Brin, Garrett Stuck
出版情報: Cambridge : Cambridge University Press, 2002  xii, 240 p. ; 24 cm
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Introduction
Examples and basic concepts / 1:
Topological dynamics / 2:
Symbolic dynamics / 3:
Ergodic theory / 4:
Hyperbolic dynamics / 5:
Ergodicity of Anosov diffeomorphisms / 6:
Low dimensional dynamics / 7:
Complex dynamics / 8:
Measure theoretic entropy / 9:
Index
Introduction
Examples and basic concepts / 1:
Topological dynamics / 2:
3.

図書

図書
Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva ; appendix by Krzysztof P. Rybakowski
出版情報: New York : Springer, c2002  viii, 280 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 47
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4.

図書

図書
George R. Sell, Yuncheng You
出版情報: New York : Springer, c2002  xiii, 670 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 143
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Preface
The Evolution of Evolutionary Systems / 1:
Dynamical Systems: Basic Theory / 2:
Linear Semigroups / 3:
Basic Theory of Evolutionary Equations / 4:
Nonlinear Partial Differential Equations / 5:
Navier Stokes Dynamics / 6:
Basic Principles of Dynamics / 7:
Inertial Manifolds and the Reduction Principle / 8:
Appendices: Basics of Functional Analysis
Bibliography
Notation Index
Subject Index
Preface
The Evolution of Evolutionary Systems / 1:
Dynamical Systems: Basic Theory / 2:
5.

図書

図書
M.C. Irwin
出版情報: Singapore : World Scientific, c2001  xii, 259 p. ; 23 cm
シリーズ名: Advanced series in nonlinear dynamics ; v. 17
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Foreword
Preface
Introduction
The simple pendulum / I.:
A dissipative system / II.:
The spherical pendulum / III.:
Vector fields and dynamical systems / IV.:
Some Simple Examples / Chapter 1.:
Flows and homeomorphisms
Orbits
Examples of dynamical systems
Constructing systems
Properties of orbits / V.:
Appendix 1
Group actions
Equivalent Systems / Chapter 2.:
Topological conjugacy
Homeomorphisms of the circle
Flow equivalence and topological equivalence
Local equivalence
Limit sets of flows
Limit sets of homeomorphisms / VI.:
Non-wandering sets / VII.:
Appendix 2
Two topological lemmas
Oriented orbits in Hausdorff spaces
Compactification
Integration of Vector Fields / Chapter 3.:
Vector fields
Velocity vector fields and integral flows
Ordinary differential equations
Local integrals
Global integrals
Appendix 3
Integrals of perturbed vector fields
First integrals
Linear Systems / Chapter 4.:
Linear flows on R[superscript n]
Linear automorphisms of R[superscript n]
The spectrum of a linear endomorphism
Hyperbolic linear automorphisms
Hyperbolic linear vector fields
Appendix 4
Spectral Theory
Linearization / Chapter 5.:
Regular points
Hartman's theorem
Hartman's theorem for flows
Hyperbolic closed orbits
Appendix 5
Smooth linearization
Liapunov stability
The index of a fixed point
Stable Manifolds / Chapter 6.:
The stable manifold at a hyperbolic fixed point of a diffeomorphism
Stable manifold theory for flows
The generalized stable manifold theorem
Appendix 6
Perturbed stable manifolds
Stable Systems / Chapter 7.:
Low dimensional systems
Anosov systems
Characterization of structural stability
Density
Omega stability
Bifurcation
Theory of Manifolds / Appendix A.:
Topological manifolds
Smooth manifolds and maps
Smooth vector bundles
The tangent bundle
Immersions, embeddings and submersions
Sections of vector bundles
Tensor bundles
Riemannian manifolds / VIII.:
Map Spaces / Appendix B.:
Spaces of smooth maps
Composition theorems
Spaces of sections
Spaces of dynamical systems
The Contraction Mapping Theorem / Appendix C.:
Bibliography
Subject Index
Foreword
Preface
Introduction
6.

図書

図書
edited by Henk W Broer, Bernd Krauskopf and Gert Vegter
出版情報: Bristol, [Eng.] : Institute of Physics Pub., c2001  xiv, 464 p. ; 25 cm
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7.

図書

図書
Valentin Afraimovich and Sze-Bi Hsu
出版情報: Providence : American Mathematical Society : International Press, c2003  ix, 353 p. ; 26 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 28
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8.

図書

図書
Clark Robinson
出版情報: Boca Raton, Fla. : CRC Press, c1999  506 p. ; 27 cm
シリーズ名: Studies in advanced mathematics
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9.

図書

図書
Ioannis Antoniou and Günter Lumer (editors)
出版情報: Boca Raton, Fla. ; London : Chapman & Hall/CRC Press, c1999  378 p. ; 26 cm
シリーズ名: Research notes in mathematics ; 399
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10.

図書

図書
Graham Everest, Thomas Ward
出版情報: London ; New York ; Tokyo : Springer, c1999  xii, 211 p. ; 24 cm
シリーズ名: Universitext
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11.

図書

図書
Saber N. Elaydi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2000  xiii, 355 p. ; 25 cm
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List of Symbols
Preface
The Stability of One-Dimensional Maps / 1:
Maps vs. Difference Equations / 1.1:
Maps vs. Differential Equations / 1.2:
Linear Maps/Difference Equations / 1.3:
Fixed (Equilibrium) Points / 1.4:
Graphical Iteration and Stability / 1.5:
Criteria for Stability / 1.6:
Hyperbolic Fixed Points / 1.6.1:
Nonhyperbolic Fixed Points / 1.6.2:
Periodic Points and their Stability / 1.7:
The Period-Doubling Route to Chaos / 1.8:
Fixed Points / 1.8.1:
2-Cycles / 1.8.2:
2[superscript 2]-Cycles / 1.8.3:
Beyond [mu][characters not reproducible] / 1.8.4:
Applications / 1.9:
A Genotype Selection Model / 1.9.1:
Sharkovsky's Theorem and Bifurcation / 2:
The Mystery of Period 3 / 2.1:
Converse of Sharkovsky's Theorem / 2.2:
Basin of Attraction / 2.3:
The Schwarzian Derivative / 2.4:
Bifurcation / 2.5:
The Lorenz Map / 2.6:
Appendix
Chaos in One Dimension / 3:
Introduction / 3.1:
Metric Spaces / 3.2:
Transitivity / 3.3:
Sensitive Dependence and Liapunov Exponents / 3.4:
Definition of Chaos / 3.5:
Symbolic Dynamics / 3.6:
Conjugacy / 3.7:
Stability of Two-Dimensional Maps / 4:
Linear Maps vs. Linear Systems / 4.1:
Computing A[superscript n] / 4.2:
Fundamental Set of Solutions / 4.3:
Second-Order Difference Equations / 4.4:
Phase Space Diagrams / 4.5:
Stability Notions / 4.6:
Stability of Linear Systems / 4.7:
Liapunov Functions for Nonlinear Maps / 4.8:
Linear Systems Revisited / 4.9:
Stability via Linearization / 4.10:
The Hartman-Grobman Theorem / 4.10.1:
The Stable Manifold Theorem / 4.10.2:
The Kicked Rotator and the Henon Map / 4.11:
The Henon Map / 4.11.2:
Discrete Epidemic Model for Gonorrhea / 4.11.3:
Perennial Grass / 4.11.4:
Chaos in Two Dimensions / 5:
Hyperbolic Anosov Toral Automorphism / 5.1:
Subshifts of Finite Type / 5.2:
The Horseshoe and Henon Maps / 5.3:
The Henon Map Revisited / 5.3.1:
Center Manifolds / 5.4:
Neimark-Sacker (Hopf) Bifurcation / 5.5:
Fractals / 6:
Examples of Fractals / 6.1:
The Dimension of a Fractal / 6.2:
Iterated Function System / 6.3:
Mathematical Foundation of Fractals / 6.4:
The Collage Theorem and Image Compression / 6.5:
The Julia and Mandelbrot Sets / 7:
Mapping by Functions on the Complex Domain / 7.1:
The Riemann Sphere / 7.2:
The Julia Set / 7.3:
Topological Properties of the Julia Set / 7.4:
Newton's Method in the Complex Plane / 7.5:
The Mandelbrot Set / 7.6:
Bibliography
Answers to Selected Problems
Index
List of Symbols
Preface
The Stability of One-Dimensional Maps / 1:
12.

図書

図書
Gerhard Keller
出版情報: Cambridge : Cambridge University Press, 1998  ix, 178 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 42
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13.

図書

図書
Folkmar Bornemann
出版情報: Berlin ; New York : Springer, c1998  xii, 156 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1687
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14.

図書

図書
edited by Silvio Levy
出版情報: Cambridge : Cambridge University Press, 1997  ix, 194 p. ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 31
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15.

図書

図書
S. Morosawa ... [et al.]
出版情報: Cambridge ; New York : Cambridge University Press, c2000  xi, 338 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; v. 66
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16.

図書

図書
L. Lerman, G. Polotovskiĭ, L. Shilnikov, editors
出版情報: Providence, R.I. : American Mathematical Society, c2000  viii, 196 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 200 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 48
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Evgeniya Aleksandrovna Leontovich-Andronova (1905-1996) / L. P. Shilnikov
On the abundance of traveling waves in coupled expanding circle maps / V. Afraimovich ; M. Courbage
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve / S. A. Alekseeva
Collapse and continuity of geodesic frameworks of surface foliations / S. Aranson ; V. Medvedev ; E. Zhuzhoma
Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps / V. N. Belykh
On the mutual arrangement of a conic and a quintic in the real projective plane / A. A. Binstein ; G. M. Polotovskii
The structure of the boundary curve for planar controllability domains / N. N. Butenina
Orbit structure in a neighborhood of a separatrix cycle containing two saddle-foci / V. V. Bykov
Example of a blue sky catastrophe / N. Gavrilov ; A. Shilnikov
Dynamics and moduli of $\Omega$-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point / S. V. Gonchenko
Topological classification of amply situated attractors of $A$-diffeomorphisms of surfaces / V. Z. Grines ; R. V. Plykin
A proof of Shilnikov's theorem for $C^1$-smooth dynamical systems / M. V. Shashkov ; D. V. Turaev
A new simple bifurcation of a periodic orbit of "blue sky catastrophe" type
On the splitting of the complex loop of a separatrix / V. P. Tareev
Some topological structures of quadratic systems with at least four limit cycles / A. A. E.
Torus maps from weak coupling of strong resonances / J. Guckenheimer ; I. Khibnik
Isoenergetical structure of integrable Hamiltonian systems in an extended neighborhood of a simple singular point: Three degrees of freedom / L. M. Lerman
Evgeniya Aleksandrovna Leontovich-Andronova (1905-1996) / L. P. Shilnikov
On the abundance of traveling waves in coupled expanding circle maps / V. Afraimovich ; M. Courbage
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve / S. A. Alekseeva
17.

図書

図書
Carmen Chicone, Yuri Latushkin
出版情報: Providence, RI : American Mathematical Society, c1999  x, 361 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; vol. 70
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Introduction
Semigroups on Banach spaces and evolution semigroups
Evolution families and Howland semigroups
Characterizations of dichotomy for evolution families
Two applications of evolution semigroups
Linear skew-product flows and Mather evolution semigroups
Characterizations of dichotomy for linear skew-product flows
Evolution operators and exact Lyapunov exponents
Bibliography
List of notations
Index
Introduction
Semigroups on Banach spaces and evolution semigroups
Evolution families and Howland semigroups
18.

図書

図書
by Pei-Chu Hu and Chung-Chun Yang
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic, c1999  ix, 338 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 483
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19.

図書

図書
by L.V. Bogdanov
出版情報: Dordrecht ; Boston : Kluwer Academic, c1999  xii, 264 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 493
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20.

図書

図書
Anthony N. Michel, Kaining Wang, Bo Hu
出版情報: New York : Marcel Dekker, c2001  xv, 707 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 239
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Preface to the Second Edition
Preface to the First Edition
Introduction / 1.:
Dynamical Systems / 1.1:
Stability Preserving Mappings / 1.2:
Stability of Motion / 1.3:
Finite Dimensional Systems / 1.4:
Infinite Dimensional Systems / 1.5:
Differential Inclusions / 1.6:
Hybrid Dynamical Systems / 1.7:
Stability of Hybrid and Discontinuous Dynamical Systems / 1.8:
Case Studies in Hybrid and Discontinuous Dynamical Systems / 1.9:
Bibliography
Notation / 2.:
Ordinary Differential Equations / 2.2:
Ordinary Difference Equations / 2.4:
Ordinary Differential Inequalities / 2.5:
Ordinary Difference Inequalities / 2.6:
Functional Differential Equations / 2.7:
Volterra Integrodifferential Equations / 2.8:
Semigroups / 2.9:
Partial Differential Equations / 2.10:
Notes and References / 2.11:
Problems / 2.12:
Invariant Sets / 3.:
Qualitative Characterizations / 3.2:
Comparison Theorems / 3.3:
Applications / 3.5:
A Perspective / 3.6:
Systems of Differential and Difference Inequalities as Comparison Systems / 3.7:
Results Involving Quasimonotonicity Conditions: Continuous-Time Case / 4.2:
Results Involving Monotonicity Conditions: Discrete-Time Case / 4.3:
The Principal Lyapunov Theorems for General Dynamical Systems / 4.4:
Converse Theorems / 4.5:
Autonomous Systems / 4.6:
Invariance Theory / 4.7:
Uniqueness of Motions / 4.8:
Lyapunov Functions and Stability Preserving Mappings / 4.9:
Applications to Discrete Event Systems / 4.10:
Preliminaries / 4.11:
Stability and Boundedness / 5.2:
Instability / 5.3:
Comparison Theory / 5.4:
Applications: Absolute Stability of Regulator Systems / 5.7:
Applications to Artificial Neural Networks / 5.8:
Applications to Digital Filters / 5.9:
Hybrid Systems / 5.10:
An Application to Artificial Neural Networks with Time Delays / 6.8:
Application to a Multicore Nuclear Reactor Model / 6.9:
Stability Analysis / 6.10:
Dynamical Systems Determined by Differential Inequalities / 7.3:
Applications to Robust Stability / 7.5:
Applications to Absolute Stability of Regulator Systems / 7.6:
Applications to a Class of Nonlinear Circuits and Artificial Neural Networks / 7.7:
A Model for General Hybrid Dynamical Systems / 7.8:
Some Examples of Hybrid Dynamical Systems Defined on Generalized Time / 8.2:
Some Qualitative Characterizations of Hybrid Dynamical Systems / 8.3:
Embedding of Hybrid Dynamical Systems into Dynamical Systems Defined on Real Time R[superscript +] / 8.4:
Some Examples of Hybrid Dynamical Systems Defined on R[superscript +] / 8.5:
Stability of Discontinuous Dynamical Systems: Results Involving Stability Preserving Mappings / 8.6:
The Principal Lyapunov Theorems for Discontinuous Dynamical Systems / 9.2:
Results Involving Vector Lyapunov Functions / 9.3:
Interconnected Systems / 9.5:
Some Qualitative Properties of Sampled-Data Control Systems / 9.6:
Stability Analysis of Multirate Digital Control Systems / 10.2:
Stability Analysis of Pulse-Width-Modulated Feedback Control Systems / 10.3:
A Class of Variable Structure Systems: Hopfield Neural Nets with Infinite Gain Amplifiers / 10.4:
Dynamical Systems Subjected to State Saturation Constraints / 10.5:
Index / 10.6:
Preface to the Second Edition
Preface to the First Edition
Introduction / 1.:
21.

図書

図書
Patrice Le Calvez ; translated by Philippe Mazaud
出版情報: Providence, R.I. : American Mathematical Society , [Paris] : Société Mathématique de France, c2000  ix, 105 p. ; 26 cm
シリーズ名: SMF/AMS texts and monographs ; v. 4
Astérisque ; no 204 (1991)
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Presentation and comparison of the different approaches to the theory of monotone twist diffeomorphisms of the annulus
Generating phases of the diffeomorphisms of the torus and the annulus
Index
Bibliography
Presentation and comparison of the different approaches to the theory of monotone twist diffeomorphisms of the annulus
Generating phases of the diffeomorphisms of the torus and the annulus
Index
22.

図書

図書
L.A. Bunimovich ... [et al.] ; edited by Ya.G. Sinai
出版情報: Berlin ; Tokyo : Springer-Verlag, c2000  x, 459 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 100 . Mathematical physics ; 1
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General Ergodic Theory of Groupsof Measure Preserving Transformations / I:
Ergodic Theory of Smooth Dynamical Systems / II:
Dynamical Systems on Homogeneous Spaces / III:
The Dynamics of Billiard Flowsin Rational Polygons / IV:
Dynamical Systemsof Statistical Mechanics and Kinetic Equations / V:
Subject Index
Basic Notions of Ergodic Theory and Examples of Dynamical Systems / I.P. Kornfeld ; Ya.G. SinaiChapter 1:
Dynamical Systems with Invariant Measures /   1:
First Corollaries of the Existence of Invariant Measures. Ergodic Theorems /   2:
Ergodicity. Decomposition into Ergodic Components. Various Mixing Conditions /   3:
General Constructions /   4:
Direct Products of Dynamical Systems / 4.1:
Skew Products of Dynamical Systems / 4.2:
Factor-Systems / 4.3:
Integral and Induced Automorphisms / 4.4:
Special Flows and Special Representations of Flows / 4.5:
Natural Extensions of Endomorphisms / 4.6:
Spectral Theory of Dynamical Systems / Chapter 2:
Groups of Unitary Operators and Semigroups of Isometric Operators Adjoint to Dynamical Systems
The Structure of the Dynamical Systems with Pure Point and Quasidiscrete Spectra
Examples of Spectral Analysis of Dynamical Systems
Spectral Analysis of Gauss Dynamical Systems
Entropy Theory of Dynamical Systems / Chapter 3:
Entropy and Conditional Entropy of a Partition
Entropy of a Dynamical System
The Structure of Dynamical Systems of Positive Entropy
The Isomorphy Problem for Bernoulli Automorphisms and K-Systems
Equivalence of Dynamical Systems in the Sense of Kakutani /   5:
Shifts in the Spaces of Sequences and Gibbs Measures /   6:
Periodic Approximations and Their Applications. Ergodic Theorems, Spectral and Entropy Theory for the General Group Actions / A.M. VershikChapter 4:
Approximation Theory of Dynamical Systems by Periodic Ones. Flows on the Two-Dimensional Torus
Flows on the Surfaces of Genus p ≥ 1 and Interval Exchange Transformations
General Group Actions
Introduction / 3.1:
General Definition of the Actions of Locally Compact Groups on Lebesgue Spaces / 3.2:
Ergodic Theorems / 3.3:
Spectral Theory / 3.4:
Entropy Theory for the Actions of General Groups
Trajectory Theory / Chapter 5:
Statements of Main Results
Sketch of the Proof. Tame Partitions
Trajectory Theory for Amenable Groups
Trajectory Theory for Non-Amenable Groups. Rigidity
Concluding Remarks. Relationship Between Trajectory Theory and Operator Algebras
Bibliography
Additional Bibliography
Ergodic Theory of SmoothDynamical Systems
Stochasticity of Smooth Dynamical Systems. The Elements of KAM-Theory / Chapter 6:
Integrable and Nonintegrable Smooth Dynamical Systems. The Hierarchy of Stochastic Properties of Deterministic Dynamics
The Kolmogorov-Arnold-Moser Theory (KAM-Theory)
General Theory of Smooth Hyperbolic Dynamical Systems / Ya.B.PesinChapter 7:
Hyperbolicity of Individual Trajectories
Introductory Remarks / 1.1:
Uniform Hyperbolicity / 1.2:
Nonuniform Hyperbolicity / 1.3:
Local Manifolds / 1.4:
Global Manifolds / 1.5:
Basic Classes of Smooth Hyperbolic Dynamical Systems. Definitions and Examples
Anosov Systems / 2.1:
Hyperbolic Sets / 2.2:
Locally Maximal Hyperbolic Sets / 2.3:
Axiom A-Diffeomorphisms / 2.4:
Hyperbolic Attractors. Repellers / 2.5:
Partially Hyperbolic Dynamical Systems / 2.6:
Mather Theory / 2.7:
Nonuniformely Hyperbolic Dynamical Systems. Lyapunov Exponents / 2.8:
Ergodic Properties of Smooth Hyperbolic Dynamical Systems
u-Gibbs Measures
Symbolic Dynamics
Measures of Maximal Entropy
Construction of u-Gibbs Measures
Topological Pressure and Topological Entropy / 3.5:
Properties of u-Gibbs Measures / 3.6:
Small Stochastic Perturbations / 3.7:
Equilibrium States and Their Ergodic Properties / 3.8:
Ergodic Properties of Dynamical Systems with Nonzero Lyapunov Exponents / 3.9:
Ergodic Properties of Anosov Systems and of UPH-Systems / 3.10:
Continuous Time Dynamical Systems / 3.11:
Hyperbolic Geodesic Flows
Manifolds with Negative Curvature
Riemannian Metrics Without Conjugate (or Focal) Points
Entropy of Geodesic Flows
Riemannian Metrics of Nonpositive Curvature
Geodesic Flows on Manifolds with Constant Negative Curvature
Dimension-like Characteristics of Invariant Sets for Dynamical Systems
Hausdorff Dimension / 6.1:
Other Dimension Characteristics / 6.3:
Carathéodory Dimension Structure. Carathéodory Dimension Characteristics / 6.4:
Examples of C-structures and Carathéodory Dimension Characteristics / 6.5:
Multifractal Formalism / 6.6:
Coupled Map Lattices /   7:
Additional References
Billiards and Other Hyperbolic Systems / L.A. BunimovichChapter 8:
Billiards
The General Definition of a Billiard
Billiards in Polygons and Polyhedrons
Billiards in Domains with Smooth Convex Boundary
Dispersing or Sinai Billiards
The Lorentz Gas and Hard Spheres Gas
Semi-dispersing Billiards and Boltzmann Hypotheses / 1.6:
Billiards in Domains with Boundary Possessing Focusing Components / 1.7:
Hyperbolic Dynamical Systems with Singularities (a General Approach) / 1.8:
Markov Approximations and Symbolic Dynamics for Hyperbolic Billiards / 1.9:
Statistical Properties of Dispersing Billiards and of the Lorentz Gas / 1.10:
Transport Coefficients for the Simplest Mechanical Models / 1.11:
Strange Attractors
Definition of a Strange Attractor
The Lorenz Attractor
Some Other Examples of Hyperbolic Strange Attractors
Ergodic Theory of One-Dimensional Mappings / M.V. JakobsonChapter 9:
Expanding Maps
Definitions, Examples, the Entropy Formula
Walters Theorem
Absolutely Continuous Invariant Measures for Nonexpanding Maps
Some Examples
Intermittency of Stochastic and Stable Systems
Ergodic Properties of Absolutely Continuous Invariant Measures
Feigenbaum Universality Law
The Phenomenon of Universality
Doubling Transformation
Neighborhood of the Fixed Point
Properties of Maps Belonging to the Stable Manifold of Φ
Rational Endomorphisms of the Riemann Sphere
The Julia Set and Its Complement
The Stability Properties of Rational Endomorphisms
Ergodic and Dimensional Properties of Julia Sets
Dynamical Systemson Homogeneous Spaces
Measures on homogeneous spaces / S.G. DaniChapter 10:
Examples of lattices
Ergodicity and its consequences
Isomorphisms and factors of affine automorphisms
Affine automorphisms of tori and nilmanifolds
Ergodic properties; the case of tori
Ergodic properties on nilmanifolds
Unipotent affine automorphisms
Quasi-unipotent affine automorphisms
Closed invariant sets of automorphisms
Dynamics of hyperbolic automorphisms
More on invariant sets of hyperbolic toral automorphisms
Distribution of orbits of hyperbolic automorphisms
Dynamics of ergodic toral automorphisms / 2.9:
Actions of groups of affine automorphisms / 2.10:
Group-induced translation flows; special cases
Flows on solvmanifolds
Homogeneous spaces of semisimple groups
Flows on low-dimensional homogeneous spaces
Ergodic properties of flows on general homogeneous spaces
Horospherical subgroups and Mautner phenomenon
Ergodicity of one-parameter flows
Invariant functions and ergodic decomposition
Actions of subgroups
Duality
Spectrum and mixing of group-induced flows
Mixing of higher orders / 4.7:
Entropy / 4.8:
K-mixing, Bernoullicity / 4.9:
Group-induced flows with hyperbolic structure
Anosov automorphisms / 5.1:
Affine automorphisms with a hyperbolic fixed point / 5.2:
Anosov flows / 5.3:
Invariant measures of group-induced flows
Invariant measures of Ad-unipotent flows
Invariant measures and epimorphic subgroups
Invariant measures of actions of diagonalisable groups
A weak recurrence property and infinite invariant measures
Distribution of orbits and polynomial trajectories
A uniform version of uniform distribution
Distribution of translates of closed orbits / 6.7:
Orbit closures of group-induced flows
Homogeneity of orbit closures / 7.1:
Orbit closures of horospherical subgroups / 7.2:
Orbits of reductive subgroups / 7.3:
Orbit closures of one-parameter flows / 7.4:
Dense orbits and minimal sets of flows / 7.5:
Divergent trajectories of flows / 7.6:
Bounded orbits and escapable sets / 7.7:
Duality and lattice-actions on vector spaces /   8:
Duality between orbits / 8.1:
Duality of invariant measures / 8.2:
Applications to Diophantine approximation /   9:
Polynomials in one variable / 9.1:
Values of linear forms / 9.2:
Diophantine approximation with dependent quantities / 9.3:
Values of quadratic forms / 9.4:
Forms of higher degree / 9.5:
Integral points on algebraic varieties / 9.6:
Classification and related questions /   10:
Metric isomorphisms and factors / 10.1:
Metric rigidity / 10.2:
Topological conjugacy / 10.3:
Topological equivalence / 10.4:
The Dynamics of Billiard Flows in Rational Polygons of Dynamical Systems / J. SmillieChapter 11:
Two Examples
Formal Properties of the Billiard Flow
The Flow in a Fixed Direction
Billiard Techniques: Minimality and Closed Orbits
Billiard Techniques: Unique Ergodicity
Dynamics on Moduli Spaces
The Lattice Examples of Veech
Dynamical Systems of Statistical Mechanicsand Kinetic Equations
Dynamical Systems of Statistical Mechanics / R.L. Dobrushin ; Yu.M. SukhovChapter 12:
Phase Space of Systems of Statistical Mechanics and Gibbs Measures
The Configuration Space
Poisson Measures
The Gibbs Configuration Probability Distribution
Potential of the Pair Interaction. Existence and Uniqueness of a Gibbs Configuration Probability Distribution
The Phase Space. The Gibbs Probability Distribution
Gibbs Measures with a General Potential
The Moment Measure and Moment Function
Dynamics of a System of Interacting Particles
Statement of the Problem
Construction of the Dynamics and Time Evolution
Hierarchy of the Bogolyubov Equations
Equilibrium Dynamics
Definition and Construction of Equilibrium Dynamics
The Gibbs Postulate
Degenerate Models
Asymptotic Properties of the Measures Pt
Ideal Gas and Related Systems
The Poisson Superstructure
Asymptotic Behaviour of the Probability Distribution Pt as t → ∞
The Dynamical System of One-Dimensional Hard Rods
Kinetic Equations
The Boltzmann Equation
The Vlasov Equation
The Landau Equation
Hydrodynamic Equations
Existence and Uniqueness Theorems for the Boltzmann Equation / N.B. MaslovaChapter 13:
Formulation of Boundary Problems. Properties of Integral Operators
Formulation of Boundary Problems
Properties of the Collision Integral
Linear Stationary Problems
Asymptotics
Internal Problems
External Problems
Kramers' Problem
Nonlinear Stationary Problems
Non-Stationary Problems
General Ergodic Theory of Groupsof Measure Preserving Transformations / I:
Ergodic Theory of Smooth Dynamical Systems / II:
Dynamical Systems on Homogeneous Spaces / III:
23.

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図書
Karl-Georg Schlesinger
出版情報: Harlow, Essex, England : Longman, 1997  116 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 372
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24.

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図書
Yakov B. Pesin
出版情報: Chicago, Ill. : University of Chicago Press, c1997  xi, 304 p. ; 23 cm
シリーズ名: Chicago lectures in mathematics
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Preface
Introduction
Carathéodory Dimension Characteristics / Part I:
General Carathéodory Construction / Chapter 1:
Carathéodory Dimension of Sets / 1:
Carathéodory Capacity of Sets / 2:
Carathéodory Dimension and Capacity of Measures / 3:
Coincidence of Carathéodory Dimension and Carathéodory Capacity of Measures / 4:
Lower and Upper Bounds for Carathéodory Dimension of Sets; Carathéodory Dimension Spectrum / 5:
C-Structures Associated with Metrics: Hausdorff Dimension and Box Dimension / Chapter 2:
Hausdorff Dimension and Box Dimension of Sets / 6:
Hausdorff Dimension and Box Dimension of Measures; Pointwise Dimension; Mass Distribution Principle / 7:
C-Structures Associated with Metrics and Measures: Dimension Spectra / Chapter 3:
q-Dimension and q-Box Dimension of Sets / 8:
q-Dimension and q-Box Dimension of Measures / 9:
Hausdorff (Box) Dimension and Q-(Box) Dimension of Sets and Measures in General Metric Spaces / Appendix I:
C-Structures Associated with Dynamical Systems: Thermodynamic Formalism / Chapter 4:
A Modification of the General Carathéodory Construction / 10:
Dimensional Definition of Topological Pressure; Topological and Measure-Theoretic Entropies / 11:
Non-additive Thermodynamic Formalism / 12:
Variational Principle for Topological Pressure; Symbolic Dynamical Systems; Bowen's Equation / Appendix II:
An Example of Carathéodory Structure Generated by Dynamical Systems / Appendix III:
Applications to Dimension Theory and Dynamical Systems / Part II:
Dimension of Cantor-like Sets and Symbolic Dynamics / Chapter 5:
Moran-like Geometric Constructions with Stationary (Constant) Ratio Coefficients / 13:
Regular Geometric Constructions / 14:
Moran-like Geometric Constructions with Non-stationary Ratio Coefficients / 15:
Geometric Constructions with Rectangles; Non-coincidence of Box Dimension and Hausdorff Dimension of Sets / 16:
Multifractal Formalism / Chapter 6:
Correlation Dimension / 17:
Dimension Spectra: Hentschel-Procaccia, Rényi, and f(alpha)-Spectra; Information Dimension / 18:
Multifractal Analysis of Gibbs Measures on Limit Sets of Geometric Constructions / 19:
Dimension of Sets and Measures Invariant under Hyperbolic Systems / Chapter 7:
Hausdorff Dimension and Box Dimension of Conformal Repellers for Smooth Expanding Maps / 20:
Multifractal Analysis of Gibbs Measures for Smooth Conformal Expanding Maps / 21:
Hausdorff Dimension and Box Dimension of Basic Sets for Axiom A Diffeomrophisms / 22:
Hausdorff Dimension of Horseshoes and Solenoids / 23:
Multifractal Analysis of Equilibrium Measures on Basic Sets of Axiom A Diffeomorphisms / 24:
A General Concept of Multifractal Spectra; Multifractal Rigidity / Appendix IV:
Relations between Dimension, Entropy, and Lyapunov Exponents / Chapter 8:
Existence and Non-existence of Pointwise Dimension for Invariant Measures / 25:
Dimension of Measures with Non-zero Lyapunov Exponents; The Eckmann-Ruelle Conjecture / 26:
Some Useful Facts / Appendix V:
Bibliography
Index
Preface
Introduction
Carathéodory Dimension Characteristics / Part I:
25.

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図書
V.V. Kozlov
出版情報: Berlin ; Tokyo : Springer Verlag, c2003  viii, 184 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 67 . Dynamical systems ; 10
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Introduction
Hydrodynamics, Geometrical Optics, and Classical Mechanics / 1:
General Vortex Theory / 2:
Geodesics on Lie Groups with Left-Invariant Metrics / 3:
Vortex Method of Integration of Hamilton Equations / 4:
Invariants of Vorticity and Second Hydrodynamics / Appendix 1:
Quantum Mechanics and Hydrodynamics / Appendix 2:
References
Index
Introduction
Hydrodynamics, Geometrical Optics, and Classical Mechanics / 1:
General Vortex Theory / 2:
26.

図書

図書
Benoit B. Mandelbrot ; with a foreword by P.W. Jones and texts co-authored by C.J.G. Evertsz and M.C. Gutzwiller
出版情報: New York : Springer, c2004  xii, 308 p. ; 24 cm
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Foreword / Peter W. Jones (2003)
Preface (2003)
Quadratic Julia and Mandelbrot Sets / I:
Introduction to papers on quadratic dynamics: a progression from seeing to discovering (2003) / C1:
Acknowledgments related to quadratic dynamics (2003) / C2:
Fractal aspects of the iteration of z to [lambda] z (1-z) for complex [lambda] and z (M1980n) / C3:
Cantor and Fatou dusts; self-squared dragons (M 1982F) / C4:
The complex quadratic map and its M-set (M1983p) / C5:
Bifurcation points and the "n squared" approximation and conjecture (M1985g) / C6:
The "normalized radical" of the M-set (M1985g) / C7:
The boundary of the M-set is of dimension 2 (M1985g) / C8:
Certain Julia sets include smooth components (M1985g) / C9:
Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (M1985g) / C10:
Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (M1985n) / C11:
Nonquadratic Rational Dynamics / II:
Introduction to chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2003) / C12:
The map z to [lambda] (z + 1/ z) and roughening of chaos from linear to planar (computer-assisted homage to K. Hokusai) (M1984k) / C13:
Two nonquadratic rational maps, devised from Weierstrass doubling formulas (1979-2003) / C14:
Iterated Nonlinear Function Systems and the Fractal Limit Sets of Kleinian Groups / III:
Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments (2003) / C15:
Self-inverse fractals, Apollonian nets, and soap (M 1982F) / C16:
Symmetry by dilation or reduction, fractals, roughness (M2002w) / C17:
Self-inverse fractals osculated by sigma-discs and limit sets of inversion ("Kleinian") groups (M1983m) / C18:
Multifractal Invariant Measures / IV:
Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2003) / C19:
Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988) / C20:
The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (M1993s) / C21:
Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) / C22:
Background and History / V:
The inexhaustible function z squared plus c (1982-2003) / C23:
The Fatou and Julia stories (2003) / C24:
Mathematical analysis while in the wilderness (2003) / C25:
Cumulative Bibliography
Index
Foreword / Peter W. Jones (2003)
Preface (2003)
Quadratic Julia and Mandelbrot Sets / I:
27.

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図書
Markus Kirkilionis ... [et al.] (eds.)
出版情報: Berlin ; Tokyo : Springer, c2003  xv, 419 p. ; 24 cm
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28.

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図書
N. Aoki, K. Hiraide
出版情報: Amsterdam ; Tokyo : North-Holland, 1994  viii, 416 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 52
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29.

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図書
M.G. Nadkarni
出版情報: Basel ; Boston : Birkhauser, 1998  vii, 182 p. ; 24 cm
シリーズ名: Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft
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30.

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図書
James Murdock
出版情報: New York ; Tokyo : Springer, c2003  xix, 494 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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Two Examples
The Splitting Problem for Linear Operators
Linear Normal Forms
Nonlinear Normal Forms
Geometrical Structures in Normal Forms
Selected Topics in Local Bifurcation Theory
Two Examples
The Splitting Problem for Linear Operators
Linear Normal Forms
31.

図書

図書
edited by J.C. Robinson and P.A. Glendinning
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xiii, 215 p. ; 25 cm
シリーズ名: NATO science series ; Sub-series II, Mathematics, physics and chemistry ; v. 19
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Preface
List of Contributors
Introduction / J.C. Robinson ; P.A. Glendinning
Spatial correlations and local fluctuations in host-parasite models / M.J. Keeling ; D.A. Rand
Lattice dynamical systems / L.A. Bunimovich ; C. Giberti
Attractors and dynamics in partial differential equations / J.K. Hale
Nonlinear dynamics of extended systems / P. Collet
Three lectures on mathematical fluid mechanics / P. Constantin
Low-dimensional models of turbulence / P.J. Holmes ; J.C. Mattingly ; R.W. Wittenberg
Preface
List of Contributors
Introduction / J.C. Robinson ; P.A. Glendinning
32.

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図書
Yuri Kifer
出版情報: Boston ; Basel : Birkhäuser, 1988  294 p. ; 24 cm
シリーズ名: Progress in probability and statistics ; v. 16
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33.

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図書
M.C. Irwin
出版情報: London ; New York ; Tokyo : Academic Press, 1980  x, 259 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 94
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34.

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図書
Jack K. Hale
出版情報: Providence, R.I. : American Mathematical Society, c1988  ix, 198 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; no. 25
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35.

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図書
Bernd Aulbach
出版情報: Berlin ; New York : Springer-Verlag, 1984  ix, 142 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1058
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36.

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図書
by George D. Birkhoff
出版情報: New York ; Providence, R.I. : American Mathematical Society, 1966  xii, 305 p. ; 24 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 9
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Physical aspects of dynamical systems Variational principles and applications
Formal aspects of dynamics
Stability of periodic motions
Existence of periodic motions
Application of Poincare's geometric theorem
General theory of dynamical systems
The case of two degrees of freedom
The problem of three bodies
Addendum Footnotes
Bibliography
Index
Physical aspects of dynamical systems Variational principles and applications
Formal aspects of dynamics
Stability of periodic motions
37.

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図書
Roger Temam
出版情報: New York : Springer, c1997  xxi, 648 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 68
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38.

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図書
Richard E. Williamson
出版情報: New York : McGraw-Hill, c1997  xiii, 690 p. ; 27 cm
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39.

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図書
Michael Blank
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 161 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 161
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Introduction
Operator approach in chaotic dynamics / Chapter 1:
Random perturbations of dynamical systems / Chapter 2:
Weakly coupled dynamical systems / Chapter 3:
Phase space discretization in dyanmical systems / Chapter 4:
Ergodic properties of some methods for numerical modeling of chaotic dynamics / Chapter 5:
References / Chapter 6:
Index
Introduction
Operator approach in chaotic dynamics / Chapter 1:
Random perturbations of dynamical systems / Chapter 2:
40.

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図書
Igor V. Novozhilov
出版情報: Boston : Birkhäuser, 1997  x, 231 p. ; 25 cm
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41.

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図書
Nguyen Dinh Cong
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1997  viii, 203 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
Oxford science publications
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42.

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図書
Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
出版情報: New York : Springer, c1996  xvii, 603 p., [8] p. of plates ; 24 cm
シリーズ名: Textbooks in mathematical sciences
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43.

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図書
J.-P. Demailly ... [et al.] ; editors, F. Catanese, C. Ciliberto
出版情報: Berlin ; New York : Springer Verlag, c1996  [v], 258 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1646 . Fondazione C.I.M.E., Firenze / adviser, Roberto Conti
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44.

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図書
by S.T. Zavalishchin and A.N. Sesekin
出版情報: Dordrecht : Kluwer Academic, c1997  xi, 256 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 394
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45.

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図書
by Curtis T. McMullen
出版情報: Princeton, NJ : Princeton University Press, 1996  vii, 253 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 142
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46.

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図書
Richard A. Holmgren
出版情報: New York ; Tokyo : Springer, c1996  xv, 223 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Preface
List of Symbols
A Quick Look at Functions
The Topology of the Real Numbers
Periodic Points and Stable Sets
Sarkovskii's Theorem
Differentiability and Its Implications
Parametrized Families of Functions and Bifurcations
The Logistic Function Part I: Cantor Sets and Chaos
The Logistic Function Part II: Topological Conjugacy
The Logistic Function Part III: A Period-Doubling
The Logistic Function Part IV: Symbolic Dynamics
Newton's Method
Numerical Solutions of Differential Equations
The Dynamics of Complex Functions
The Quadratic Family and the Mandelbrot Set
Appendix Mathematica Algorithms
References
Index
Preface
List of Symbols
A Quick Look at Functions
47.

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図書
by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan
出版情報: Dordrecht : Kluwer, c1996  x, 285 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 370
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48.

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図書
Ferdinand Verhulst
出版情報: Berlin ; Tokyo : Springer Verlag, c1996  x, 303 p. ; 24 cm
シリーズ名: Universitext
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49.

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図書
Yurii A. Kravtsov, James B. Kadtke (eds.)
出版情報: Berlin : Springer, c1996  xii, 234 p. ; 25 cm
シリーズ名: Springer series in synergetics ; 69
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50.

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図書
A.S. Fokas and I.M. Gelfand, editors
出版情報: Boston : Birkhäuser, c1997  viii, 350 p. ; 26 cm
シリーズ名: Progress in nonlinear differential equations and their applications / editor, Haim Brezis ; v. 26
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51.

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図書
Khalid Alhumaizi and Rutherford Aris
出版情報: Harlow : Longman, 1995  328 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 341
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52.

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図書
G. Da Prato, J. Zabczyk
出版情報: Cambridge ; New York : Cambridge University Press, 1996  xi, 339 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 229
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Markovian Dynamical Systems / Part I:
General dynamical systems / 1:
Canonical Markovian systems / 2:
Ergodic and mixing measures / 3:
Regular Markovian systems / 4:
Invariant Measures For Stochastics For Evolution Equations / Part II:
Stochastic differential equations / 5:
Existence of invariant measures / 6:
Uniqueness of invariant measures / 7:
Densities of invariant measures / 8:
Invariant Measures For Specific Models / Part III:
Ornstein-Uhlenbeck processes / 9:
Stochastic delay systems / 10:
Reaction-diffusion equations / 11:
Spin systems / 12:
Systems perturbed through the boundary / 13:
Burgers equation / 14:
Navier-Stokes equations / 15:
Appendices
Markovian Dynamical Systems / Part I:
General dynamical systems / 1:
Canonical Markovian systems / 2:
53.

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図書
Christian Mira, ... [et al.]
出版情報: Singapore : World Scientific, c1996  xxii, 607 p. ; 23 cm
シリーズ名: World Scientific series on nonlinear science / editor, Leon O. Chua ; ser. A, v. 20
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54.

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図書
Sergei Yu. Pilyugin
出版情報: Berlin ; New York : Springer-Verlag, c1994  viii, 188 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1571
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55.

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図書
L. Arnold ... [et al.] ; editor, R. Johnson
出版情報: Berlin ; New York : Springer Verlag, c1995  vi, 329 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1609 . Fondazione C.I.M.E., Firenze / advisor, Robert Conti
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56.

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図書
D.V. Anosov (ed.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1995  235 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 66 . Dynamical systems ; 9
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目次情報:
Elliptic Boundary Problems / M.S. Agranovich
Boundary Value Problems for Elliptic Pseudodifferential Operators / A.V. Brenner ; E.M. Shargorodsky
Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary / B.A. Plamenevskij
Elliptic Boundary Problems / M.S. Agranovich
Boundary Value Problems for Elliptic Pseudodifferential Operators / A.V. Brenner ; E.M. Shargorodsky
Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary / B.A. Plamenevskij
57.

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図書
Pei-Dong Liu, Min Qian
出版情報: Berlin ; New York : Springer-Verlag, c1995  xi, 221 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1606
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58.

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図書
Giuseppe Marmo ... [et al.]
出版情報: Chichester, Sussex, England ; New York : Wiley, c1985  xii, 377 p. ; 24 cm
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59.

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図書
Pierre Collet, Jean-Pierre Eckmann
出版情報: Basel ; Boston : Birkhäuser, c1980  vii, 248 p. ; 24 cm
シリーズ名: Progress in physics ; v. 1
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60.

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図書
John Guckenheimer, Philip Holmes
出版情報: New York ; Berlin ; Tokyo : Springer, 1986, c1983  xvi, 459 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 42
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Introduction: Differential Equations and Dynamical Systems / Chapter 1:
An Introduction to Chaos: Four Examples / Chapter 2:
Local Bifurcations / Chapter 3:
Averaging and Perturbation from a Geometric Viewpoint / Chapter 4:
Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors / Chapter 5:
Global Bifurcations / Chapter 6:
Local Codimension Two Bifurcations of Flows / Chapter 7:
Appendix
Suggestions for Further Reading
Postscript Added at Second Printing
Glossary
References
Index
Introduction: Differential Equations and Dynamical Systems / Chapter 1:
An Introduction to Chaos: Four Examples / Chapter 2:
Local Bifurcations / Chapter 3:
61.

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W. Szlenk ; [translated by Marcin E. Kuczma]
出版情報: Chichester ; New York : Wiley , Warszawa : PWN-Polish Scientific Publishers, c1984  x, 369 p. ; 24 cm
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62.

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図書
Anatole Katok, Jean-Marie Strelcyn ; with the collaboration of F. Ledrappier and F. Przytycki
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  viii, 283 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1222
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63.

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図書
M.B. Sevryuk
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  v, 319 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1211
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64.

雑誌

雑誌
出版情報: New York, N.Y. : Marcel Dekker, [1992]-  v. ; 23 cm
巻次年月次: Vol. 1, no. 1 (1992/1993)-
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65.

図書

図書
Klaus Schmidt
出版情報: Basel : Birkhäuser, c1995  xviii, 310 p. ; 24 cm
シリーズ名: Progress in mathematics ; vol. 128
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66.

図書

図書
Hal L. Smith
出版情報: Providence, R.I. : American Mathematical Society, c1995  x, 174 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 41
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目次情報: 続きを見る
Introduction to the Theory of Competitive and Cooperative Systems
Monotone dynamical systems
Stability and convergence
Competitive and cooperative differential equations
Irreducible cooperative systems
Cooperative systems of delay differential equations
Nonquasimonotone delay differential equations
Quasimonotone systems of parabolic equations
A competition model
Appendix
Bibliography
Index
Introduction to the Theory of Competitive and Cooperative Systems
Monotone dynamical systems
Stability and convergence
67.

図書

図書
Torsten Bohlin
出版情報: Berlin ; Tokyo : Springer-Verlag, c1991  xii, 365 p. ; 25 cm
シリーズ名: Communications and control engineering
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68.

図書

図書
M. Eslami
出版情報: Berlin ; Tokyo : Springer-Verlag, c1994  xvii, 600 p. ; 25 cm
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69.

図書

図書
Richard A. Holmgren
出版情報: New York ; Berlin : Springer-Verlag, c1994  xi, 214 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Preface
List of Symbols
A Quick Look at Functions
The Topology of the Real Numbers
Periodic Points and Stable Sets
Sarkovskii's Theorem
Differentiability and Its Implications
Parametrized Families of Functions and Bifurcations
The Logistic Function Part I: Cantor Sets and Chaos
The Logistic Function Part II: Topological Conjugacy
The Logistic Function Part III: A Period-Doubling
The Logistic Function Part IV: Symbolic Dynamics
Newton's Method
Numerical Solutions of Differential Equations
The Dynamics of Complex Functions
The Quadratic Family and the Mandelbrot Set
Appendix Mathematica Algorithms
References
Index
Preface
List of Symbols
A Quick Look at Functions
70.

図書

図書
David Ruelle
出版情報: Providence, R.I. : American Mathematical Society, c1994  vii, 62 p. ; 27 cm
シリーズ名: CRM monograph series ; v. 4
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71.

図書

図書
Pierre N.V. Tu
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1994  xviii, 314 p. ; 25 cm
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72.

図書

図書
Derong Liu and Anthony N. Michel
出版情報: London ; Berlin ; New York : Springer-Verlag, c1994  xiv, 191 p. ; 24 cm
シリーズ名: Lecture notes in control and information sciences ; 195
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73.

図書

図書
Clark Robinson
出版情報: Boca Raton ; Tokyo : CRC Press, c1995  468 p. ; 27 cm
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74.

図書

図書
Krzysztof Kowalski, Willi-Hans Steeb
出版情報: Singapore : World Scientific, c1991  184 p. ; 23 cm
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75.

図書

図書
by Anatoliy G. Butkovskiy
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1991  ix, 170 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 63
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76.

図書

図書
Uwe Helmke and John B. Moore ; with a foreword by R. Brockett
出版情報: London ; Tokyo : Springer-Verlag, c1994  xiv, 391 p. ; 25 cm
シリーズ名: Communications and control engineering
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77.

図書

図書
Jacob Palis, Floris Takens
出版情報: Cambridge [England] : Cambridge University Press, 1993  x, 234 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 35
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78.

図書

図書
by Jan-Erik Björk
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1993  xiii, 581 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 247
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79.

図書

図書
V.I. Arnol'd (ed.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1993  235 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 39 . Dynamical systems ; 8 . Singularity theory ; 2
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目次情報:
Singularity II
Applications / V.I. Arnol'd ; V.V. Goryunov ; O.V. Lyashko ; V.A. Vasil'ev
Singularity II
Applications / V.I. Arnol'd ; V.V. Goryunov ; O.V. Lyashko ; V.A. Vasil'ev
80.

図書

図書
Ethan Akin
出版情報: Providence, R.I. : American Mathematical Society, c1993  x, 261 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 1
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Introduction: Gradient systems
Closed relations and their dynamic extensions
Invariant sets and Lyapunov functions
Attractors and basic sets Mappings-invariant subsets and transitivity concepts
Computation of the chain recurrent set
Chain recurrence and Lyapunov functions for flows
Topologically robust properties of dynamical systems
Invariant measures for mappings Examples-circles, simplex, and symbols
Fixed points Hyperbolic sets and axiom a homeomorphisms Historical remarks
References
Subject index
Introduction: Gradient systems
Closed relations and their dynamic extensions
Invariant sets and Lyapunov functions
81.

図書

図書
Welington de Melo, Sebastian van Strien
出版情報: Berlin ; Tokyo : Springer-Verlag, c1993  xiii, 605 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 25
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82.

図書

図書
H. Brian Griffiths, Adrian Oldknow
出版情報: New York : Ellis Horwood, 1993  xiii, 435 p. ; 24 cm
シリーズ名: Ellis Horwood series in mathematics and its applications ; . Statistics, operational research, and computational mathematics
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83.

図書

図書
Antonio Ambrosetti, Vittorio Coti Zelati
出版情報: Boston : Birkhäuser, c1993  xii, 157 p. ; 25 cm
シリーズ名: Progress in nonlinear differential equations and their applications ; v. 10
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84.

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図書
Freddy Dumortier, Paulo R. Rodrigues, Robert Roussarie
出版情報: Berlin ; New York : Springer-Verlag, 1981  iv, 197 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 902
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85.

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図書
Roel Nottrot
出版情報: Berlin ; New York : Springer-Verlag, 1982  vi, 124 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 963
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86.

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Jacob Palis, Jr., Welington de Melo ; translated by A.K. Manning
出版情報: New York ; Berlin : Springer, 1982  xii, 198 p. ; 24 cm
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87.

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図書
Roger Temam
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xvi, 500 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 68
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88.

図書

図書
Hao Bai-lin
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1989  xv, 460 p. ; 23 cm
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89.

図書

図書
D.D. Bainov, P.S. Simeonov
出版情報: Chichester : E. Horwood , New York : Halsted Press, 1989  255 p. ; 25 cm
シリーズ名: Ellis Horwood series in mathematics and its applications ; . Numerical analysis, statistics, and operational research
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90.

図書

図書
edited by David Chillingworth
出版情報: Berlin ; New York : Springer-Verlag, 1971  x, 173 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 206
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91.

図書

図書
Robert L. Devaney
出版情報: Redwood City, Calif. ; Tokyo : Addison-Wesley Pub. Co., c1989  xvi, 336 p., [8] p. of col. plates ; 25 cm
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92.

図書

図書
Rufus Bowen
出版情報: Berlin : Springer-Verlag, 1975  108 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 470
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93.

図書

図書
Ya.G. Sinai (ed.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  viii, 281 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 2 . Dynamical systems ; 2
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94.

図書

図書
Igor Gumowski, Christian Mira
出版情報: Berlin ; New York : Springer-Verlag, 1980  vi, 272 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 809
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95.

図書

図書
C.K.R.T. Jones, U. Kirchgraber, H.O. Walther, managing editors
出版情報: Berlin ; Tokyo : Springer-Verlag, c1992-  v. ; 24 cm
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96.

図書

図書
A.N. Leznov, M.V. Saveliev ; translated from the Russian by D.A. Leites
出版情報: Basel ; Boston : Birkhäuser Verlag, 1992  xvii, 290 p. ; 24 cm
シリーズ名: Progress in physics ; v. 15
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97.

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図書
Milan Medved̕
出版情報: Bristol, England ; Philadelphia : A. Hilger, c1992  viii, 293 p. ; 25 cm
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98.

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図書
Jack K. Hale, Hüseyin Koçak
出版情報: New York ; Tokyo : Springer-Verlag, c1991  xiv, 568 p. ; 25 cm
シリーズ名: Texts in applied mathematics ; 3
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目次情報: 続きを見る
Dimension One / Part I:
Scalar Autonomous Equations / Chapter 1:
Elementary Bifurcations / Chapter 2:
Scalar Maps / Chapter 3:
Dimension One and One Half / Part II:
Scalar Nonautonomous Equations / Chapter 4:
Bifurcation of Periodic Equations / Chapter 5:
On Tori and Circles / Chapter 6:
Dimension Two / Part III:
Planar Autonomous Systems / Chapter 7:
Linear Systems / Chapter 8:
Near Equilibria / Chapter 9:
In the Presence of a Zero Eigenvalue / Chapter 10:
In the Presence of Purely Imaginary Eigenvalues / Chapter 11:
Periodic Orbits / Chapter 12:
All Planar Things Considered / Chapter 13:
Conservative and Gradient Systems / Chapter 14:
Planar Maps / Chapter 15:
Higher Dimensions / Part IV:
Dimension Two and One Half / Chapter 16:
Dimension Three / Chapter 17:
Dimension Four / Chapter 18:
Farewell
A Catalogue of Fundamental Theorems / Appendix:
References
Index
Dimension One / Part I:
Scalar Autonomous Equations / Chapter 1:
Elementary Bifurcations / Chapter 2:
99.

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図書
Shôichirô Sakai
出版情報: Cambridge [England] ; Tokyo : Cambridge University Press, 1991  xi, 219 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 41
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目次情報: 続きを見る
Preface
Preliminaries / 1:
Bounded derivations / 2:
Unbounded derivations / 3:
C-dynamical systems / 4:
Index
Preface
Preliminaries / 1:
Bounded derivations / 2:
100.

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図書
Valeriĭ V. Kozlov, Dmitriĭ V. Treshchëv
出版情報: Providence, R.I. : American Mathematical Society, c1991  viii, 171 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 89
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目次情報: 続きを見る
Introduction to the Dynamics of Systems with Impacts
Introduction: Elements of impact theory
The genetic method in the dynamics of systems with one-sided constraints
Periodic trajectories of the Birkhoff billiard
The Hill equation
Integrable problems
Nonintegrable billiards
Systems with elastic reflections and KAM theory / Appendix I:
On the connection of dynamic and geometric properties of periodic trajectories / Appendix II:
Introduction to the Dynamics of Systems with Impacts
Introduction: Elements of impact theory
The genetic method in the dynamics of systems with one-sided constraints
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