Discrete Chaos, Second Edition

Discrete Chaos, Second Edition : With Applications in Science and Engineering

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Description

Over the last 15 years chaos has virtually exploded over the landscape of mathematics and showered its effects on nearly every scientific discipline. However, despite the large number of texts published on the subject, a need has persisted for a book accessible to readers of varying backgrounds that includes discussion of stability theory and emphasizes real-world applications.

Discrete Chaos fills that need. With only calculus and linear algebra as prerequisites, this book offers a broad range of topics with a depth not often found in texts written at this level. The author presents a thorough exposition of both stability and chaos theories in both one and two dimensions. He offers a highly readable account of fractals and the mathematics behind them, and demonstrates a number of applications from a variety of fields.

This unique treatment of chaos encourages readers to make mathematical discoveries of their own through computer experimentation. The author incorporates the use of Maplea software throughout the book to aid in the solution of problems. All of the programs used in the book can be easily downloaded from the Internet.

You'll find even the most difficult material in an elementary framework, easily accessible regardless of your background and specialization. With a multitude of exercises to further enhance the learning experience, Discrete Chaos offers the perfect vehicle for beginning the journey into the rich world of chaos.
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Product details

  • Hardback | 376 pages
  • 157 x 247.4 x 25.1mm | 666.79g
  • Chapman & Hall/CRC
  • United States
  • English
  • 965 equations; 4 Tables, black and white
  • 1584880023
  • 9781584880028

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 Henon 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
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