Discrete chaos

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Discrete chaos / Saber N. Elaydi

資料種別:: 図書
出版情報:: Boca Raton, Fla. : Chapman & Hall/CRC, c2000
形態:: xiii, 355 p. ; 25 cm
著者名:: Elaydi, Saber, 1943- <DA04775499>
ISBN:: 9781584880028 [1584880023]
書誌ID:: BA45929305

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注記:

Includes bibliographical references (p. 333-337) and index

主題:

Chaotic behavior in systems; Difference equations; Differentiable dynamical systems

言語:

英語

目次情報:

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：

Maps vs. Difference Equations / 1.1：

Maps vs. Differential Equations / 1.2：

Linear Maps/Difference Equations / 1.3：

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