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Iterates of Piecewise Monotone Mappings on an Interval

  • Book
  • © 1988

Overview

Authors:
  1. Chris Preston
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1347)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Chris Preston
    Pages 1-19

  3. Piecewise monotone mappings

    • Chris Preston
    Pages 20-33

  4. Proof of Theorems 2.4 and 2.5

    • Chris Preston
    Pages 34-40

  5. Sinks and homtervals

    • Chris Preston
    Pages 41-49

  6. Examples of register-shifts

    • Chris Preston
    Pages 50-56

  7. A proof of Parry's theoren (Theorem 2.6)

    • Chris Preston
    Pages 57-67

  8. Reductions

    • Chris Preston
    Pages 68-81

  9. The structure of the set D(f)

    • Chris Preston
    Pages 82-102

  10. Countable closed invariant sets

    • Chris Preston
    Pages 103-111

  11. Extensions

    • Chris Preston
    Pages 112-125

  12. Refinements

    • Chris Preston
    Pages 126-134

  13. Mappings with one turning point

    • Chris Preston
    Pages 135-152

  14. Some miscellaneous results from real analysis

    • Chris Preston
    Pages 153-159

  15. Back Matter

    Pages 160-166
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Keywords

About this book

Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.

Bibliographic Information

  • Book Title: Iterates of Piecewise Monotone Mappings on an Interval

  • Authors: Chris Preston

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0079769

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50329-3Published: 12 October 1988

  • eBook ISBN: 978-3-540-45971-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 172

  • Topics: Real Functions

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