Table of Contents

The Stability of One-Dimensional Maps
Maps Versus Difference Equations
Maps Versus Differential Equations
Linear Maps/Difference Equations
Fixed Points
Graphical Iteration and Stability
Criteria for Stability
Periodic Points and Their Stability
The Period-Doubling Route to Chaos
Applications
Sharkovsky's Theorem and Bifurcation
The Mystery of Period 3
Converse of Sharkovsky's Theorem
Basin of Attraction
The Schwarzian Derivative
Bifurcation
The Lorenz Map
Chaos in One Dimension
Introduction
Metric Spaces
Transitivity
Sensitive Dependence and Liapunov Exponents
Definition and Chaos
Symbolic Dynamics
Conjugacy
Stability of Two-Dimensional Maps
Linear Maps Versus Linear Systems
Computing An
Phase Space
Liapunov Functions for Nonlinear Maps
Linear Systems Revisited
Stability via Linearization
Applications
Chaos in Two Dimensions
Hyperbolic Anosov Toral Automorphism
Symbolic Dynamics
The Horseshoe and Hénon Maps
Center Manifolds
Bifurcation
Fractals
Examples of Fractals
The Dimension of Fractal
Iterated Function System
Mathematical Foundation of Fractals
The Collage Theorem and Image Compression
The Julia and Mandelbrot Sets
Mapping by Functions on the Complex Domain
The Riemann Sphere
The Julia Set
Topological Properties of the Julia Set
Newton's Method in the Complex Plane
The Mandelbrot Set
Bibliography