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: |