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1.

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:
2.

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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3.

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:
4.

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
5.

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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6.

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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7.

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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8.

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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9.

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:
10.

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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