First Course in Chaotic Dynamical Systems Theory and Experiment

ISBN-10: 0201554062
ISBN-13: 9780201554069
Edition: Revised 
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Book details

List price: $76.00
Publisher: Westview Press
Publication date: 10/21/1992
Binding: Hardcover
Pages: 320
Size: 6.75" wide x 9.75" long x 0.75" tall
Weight: 1.672
Language: English

A Mathematical and Historical Tour
Images from Dynamical Systems
A Brief History of Dynamics
Examples of Dynamical Systems
An Example from Finance
An Example from Ecology
Finding Roots and Solving Equations
Differential Equations
Orbits
Iteration
Orbits
Types of Orbits
Other Orbits
The Doubling Function
Experiment: The Computer May Lie
Graphical Analysis
Graphical Analysis
Orbit Analysis
The Phase Portrait
Fixed and Periodic Points
A Fixed Point Theorem
Attraction and Repulsion
Calculus of Fixed Points
Why Is This True?
Periodic Points
Experiment: Rates of Convergence
Bifurcations
Dynamics of the Quadratic Map
The Saddle-Node Bifurcation
The Period-Doubling Bifurcation
Experiment: The Transition to Chaos
The Quadratic Family
The Case c = -2
The Case c [actual symbol not reproducible] -2
The Cantor Middle-Thirds Set
Transition to Chaos
The Orbit Diagram
The Period-Doubling Route to Chaos
Experiment: Windows in the Orbit Diagram
Symbolic Dynamics
Itineraries
The Sequence Space
The Shift Map
Conjugacy
Chaos
Three Properties of a Chaotic System
Other Chaotic Systems
Manifestations of Chaos
Experiment: Feigenbaum's Constant
Sarkovskii's Theorem
Period 3 Implies Chaos
Sarkovskii's Theorem
The Period 3 Window
Subshifts of Finite Type
The Role of the Critical Orbit
The Schwarzian Derivative
The Critical Point and Basins of Attraction
Newton's Method
Basic Properties
Convergence and Nonconvergence
Fractals
The Chaos Game
The Cantor Set Revisited
The Sierpinski Triangle
The Koch Snowflake
Topological Dimension
Fractal Dimension
Iterated Function Systems
Experiment: Iterated Function Systems
Complex Functions
Complex Arithmetic
Complex Square Roots
Linear Complex Functions
Calculus of Complex Functions
The Julia Set
The Squaring Function
The Chaotic Quadratic Function
Cantor Sets Again
Computing the Filled Julia Set
Experiment: Filled Julia Sets and Critical Orbits
The Julia Set as a Repellor
The Mandelbrot Set
The Fundamental Dichotomy
The Mandelbrot Set
Experiment: Periods of Other Bulbs
Experiment: Periods of the Decorations
Experiment: Find the Julia Set
Experiment: Spokes and Antennae
Experiment: Similarity of the Mandelbrot and Julia Sets
Further Projects and Experiments
The Tricorn
Cubics
Exponential Functions
Trigonometric Functions
Complex Newton's Method
Appendix A. Mathematical Preliminaries
Appendix B. Algorithms
Appendix C. References
Index

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