A First Course in Discrete Dynamical Systems

  • Richard A. Holmgren

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Richard A. Holmgren
    Pages 1-8
  3. Richard A. Holmgren
    Pages 9-20
  4. Richard A. Holmgren
    Pages 21-29
  5. Richard A. Holmgren
    Pages 31-39
  6. Richard A. Holmgren
    Pages 41-46
  7. Richard A. Holmgren
    Pages 47-57
  8. Richard A. Holmgren
    Pages 59-67
  9. Richard A. Holmgren
    Pages 69-86
  10. Richard A. Holmgren
    Pages 109-126
  11. Richard A. Holmgren
    Pages 127-151
  12. Richard A. Holmgren
    Pages 153-165
  13. Richard A. Holmgren
    Pages 167-192
  14. Richard A. Holmgren
    Pages 193-202
  15. Back Matter
    Pages 203-224

About this book

Introduction

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.

Keywords

bifurcation calculus convergence differential equation dynamical systems iteration metric space real number

Authors and affiliations

  • Richard A. Holmgren
    • 1
  1. 1.Department of MathematicsAllegheny CollegeMeadvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8732-7
  • Copyright Information Springer-Verlag New York, Inc. 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94780-8
  • Online ISBN 978-1-4419-8732-7
  • Series Print ISSN 0172-5939
  • About this book