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A First Course in Discrete Dynamical Systems

  • Textbook
  • © 1994

Overview

Authors:
  1. Richard A. Holmgren

    1. Department of Mathematics, Allegheny College, Meadville, USA

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Part of the book series: Universitext (UTX)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Richard A. Holmgren
    Pages 1-7

  3. A Quick Look at Functions

    • Richard A. Holmgren
    Pages 9-19

  4. The Topology of the Real Numbers

    • Richard A. Holmgren
    Pages 21-29

  5. Periodic Points and Stable Sets

    • Richard A. Holmgren
    Pages 31-39

  6. Sarkovskii’s Theorem

    • Richard A. Holmgren
    Pages 41-46

  7. Differentiability and Its Implications

    • Richard A. Holmgren
    Pages 47-56

  8. Parametrized Families of Functions and Bifurcations

    • Richard A. Holmgren
    Pages 57-66

  9. The Logistic Function, Part I

    • Richard A. Holmgren
    Pages 67-77

  10. Symbolic Dynamics and Chaos

    • Richard A. Holmgren
    Pages 79-93

  11. The Logistic Function, Part II: Topological Conjugacy

    • Richard A. Holmgren
    Pages 95-103

  12. The Logistic Function, Part III

    • Richard A. Holmgren
    Pages 105-114

  13. Newton’s Method

    • Richard A. Holmgren
    Pages 115-139

  14. Numerical Solutions of Differential Equations

    • Richard A. Holmgren
    Pages 141-153

  15. The Dynamics of Complex Functions

    • Richard A. Holmgren
    Pages 155-180

  16. The Quadratic Family and the Mandelbrot Set

    • Richard A. Holmgren
    Pages 181-189

  17. Back Matter

    Pages 191-215
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Keywords

About this book

An increasing number of colleges and universities are offering undergradu­ ate courses in discrete dynamical systems. This growth is due in part to the proliferation of inexpensive and powerful computers, which have provided access to the interesting and complex phenomena that are at the heart of dynamics. A second reason for introducing dynamics into the undergradu­ ate curriculum is that it serves as a bridge from concrete, often algorithmic calculus courses, to the more abstract concepts of analysis and topology. Discrete dynamical systems are essentially iterated functions, and if there is one thing computers do well, it is iteration. It is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Every effort has been made to exploit this opportunity to illustrate the beauty and power of mathematics in an interesting and engaging way. This work is first and foremost a mathematics book. Individuals who read it and do the exercises will gain not only an understanding of dynamical systems, but an increased understanding of the related areas in analysis as well.

Authors and Affiliations

  • Department of Mathematics, Allegheny College, Meadville, USA

    Richard A. Holmgren

Bibliographic Information

  • Book Title: A First Course in Discrete Dynamical Systems

  • Authors: Richard A. Holmgren

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4684-0222-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • eBook ISBN: 978-1-4684-0222-3Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 214

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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