A First Course in Discrete Dynamical Systems

By: Richard Holmgren

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Paperback | 1 September 2000 | Edition Number 2

At a Glance

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244 Pages

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Revised

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24.13 x 15.88 x 1.27

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Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix.

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Preface
List of Symbols
A Quick Look at Functions
The Topology of the Real Numbers
Periodic Points and Stable Sets
Sarkovskii's Theorem
Differentiability and Its Implications
Parametrized Families of Functions and Bifurcations
The Logistic Function Part I: Cantor Sets and Chaos
The Logistic Function Part II: Topological Conjugacy
The Logistic Function Part III: A Period-Doubling
The Logistic Function Part IV: Symbolic Dynamics
Newton's Method
Numerical Solutions of Differential Equations
The Dynamics of Complex Functions
The Quadratic Family and the Mandelbrot Set
Appendix Mathematica Algorithms
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

A First Course in Discrete Dynamical Systems

At a Glance

Paperback

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How to return your order

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