A First Course in Discrete Dynamical Systems /

A First Course in Discrete Dynamical Systems / by Richard A. Holmgren.

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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...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Holmgren, Richard A.
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1996.
Edition:Second edition.
Series:Universitext.
Subjects:
Mathematics.
Global analysis (Mathematics)
Cell aggregation > Mathematics.
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.

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