close
1.

図書
図書
1. Discrete chaos
Saber N. Elaydi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2000  xiii, 355 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
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：
2.

図書
図書
2. Discreteness and continuity in problems of chaotic dynamics
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
所蔵情報: loading…
目次情報: 続きを見る
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：
3.

図書
図書
3. Surveying a dynamical system : a study of the Gray-Scott reaction in a two-phase reactor
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
所蔵情報: loading…
4.

図書
図書
4. Dynamical systems with hyperbolic behaviour (: gw ; : us)
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
所蔵情報: loading…
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
5.

図書
図書
5. Chaos : an introduction to dynamical systems
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
所蔵情報: loading…
6.

図書
図書
6. Order within chaos : towards a deterministic approach to turbulence (: us ; : fr)
Pierre Bergé, Yves Pomeau, Christian Vidal ; preface by David Ruelle ; translated from the French by Laurette Tuckerman
出版情報: New York : Wiley , Paris : Hermann, c1984  xv, 329 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
From Order
Free Oscillator--Damped Oscillator
Forced Oscillator--Parametric Oscillator
The Fourier Transform
Poincare Sections
Three Examples of Dynamical Systems
To Chaos
Temporal Chaos in Dissipative System
Strange Attractors
Quasiperiodicity
The Subharmonic Cascade
Intermittency
Debate
Appendixes
Index
From Order
Free Oscillator--Damped Oscillator
Forced Oscillator--Parametric Oscillator
7.

図書
図書
7. Chaos, dynamics, and fractals : an algorithmic approach to deterministic chaos
Joseph L. McCauley
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1993  xxi, 323 p. ; 24 cm
シリーズ名: Cambridge nonlinear science series ; 2
所蔵情報: loading…
目次情報: 続きを見る
Foreword
Introduction
Flows in phase space / 1：
Introduction to deterministic chaos / 2：
Conservative synamical systems / 3：
Fractals and fragmentation in phase space / 4：
The way to chaos by instability of quasiperiodic orbits / 5：
The way to chaos by period doubling / 6：
Multifractals / 7：
Statistical physics on chaotic symbol sequences / 8：
Universal chaotic dynamics / 9：
Intermittence in fluid dynamics / 10：
From flows to automata: chaotic systems as completely deterministic machines / 11：
References
Index
Foreword
Introduction
Flows in phase space / 1：
8.

図書
図書
8. Chaotic behaviour of deterministic dissipative systems
Miloš Marek, Igor Schreiber
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1991  x, 367 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Differential equations, maps and asymptotic behaviour / 1：
Transition from order to chaos / 2：
Numerical methods for studies of parametric dependences, bifurcations and chaos / 3：
Chaotic dynamics in experiments / 4：
Forced and coupled chemical oscillators: a case study of chaos / 5：
Chaos in distributed systems / 6：
Appendices
Bibliography
Index
Introduction
Differential equations, maps and asymptotic behaviour / 1：
Transition from order to chaos / 2：
9.

図書
図書
9. Discrete dynamical systems : theory and applications (: hard ; : pbk)
James T. Sandefur
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1990  xiii, 445 p. ; 26 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction to Dynamical Systems / 1：
First Order Linear Dynamical Systems / 2：
Introduction to Nonlinear Dynamical Systems / 3：
Complex Behavior for Nonlinear Dynamical Systems / 4：
Higher Order Linear Dynamical Systems / 5：
Dynamical Systems of Several Equations / 6：
Nonlinear Systems of Several Equations / 7：
Introduction to Dynamical Systems / 1：
First Order Linear Dynamical Systems / 2：
Introduction to Nonlinear Dynamical Systems / 3：
10.

図書
図書
10. An introduction to chaotic dynamical systems. 2nd ed
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
所蔵情報: loading…
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼