Periodic Points
Iterates of Functions
Fixed Points
Periodic Points
Families of Functions
The Quadratic Family
Bifurcations
Period-3 Points
The Schwarzian Derivative
One-Dimensional Chaos
Chaos
Transitivity and Strong Chaos
Conjugacy
Cantor Sets
Two-Dimensional Chaos
Review of Matrices
Dynamics of Linear Functions
Nonlinear Maps
The Hénon Map
The Horseshoe Map
Systems of Differential Equations
Review of Systems of Differential Equations
Almost Linearity
The Pendulum
The Lorenz System
Introduction to Fractals
Self-Similarity
The Sierpiński Gasket and Other "Monsters"
Space-Filling Curves
Similarity and Capacity Dimensions
Lyapunov Dimension
Calculating Fractal Dimensions of Objects
Creating Fractals Sets
Metric Spaces
The Hausdorff Metric
Contractions and Affine Functions
Iterated Function Systems
Algorithms for Drawing Fractals
Complex Fractals: Julia Sets and the Mandelbrot Set
Complex Numbers and Functions
Julia Sets
The Mandelbrot Set
Computer Programs
Answers to Selected Exercises
References
Index