A First Course in Discrete Dynamical Systems

Paperback | August 17, 2000

byRichard Holmgren

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Given the ease with which computers can do iteration it is now possible for almost anyone 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. Mathematica programs that illustrate the dynamics are included in an appendix.

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Given the ease with which computers can do iteration it is now possible for almost anyone 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 subj...

From the Jacket

A discrete dynamical system can be characterized as an iterated function. Given the efficiency 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 bot...

Format:PaperbackDimensions:238 pages, 9.25 × 6.1 × 0.27 inPublished:August 17, 2000Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387947809

ISBN - 13:9780387947808

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Table of Contents

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.