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Dynamical Systems V

Bifurcation Theory and Catastrophe Theory

  • Book
  • © 1994

Overview

Editors:
  1. V. I. Arnol’d

    1. Steklov Mathematical Institute, Moscow, Russia

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  • The authors are masters in fields of bifurcation theory and catastrophe theory
  • Arnol'd is known for keeping the mathematics correct and avoiding non-rigorous applications
  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Bifurcation Theory

    1. Front Matter

      Pages 1-9
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    2. Bifurcations of Equilibria

      • V. I. Arnol’d
      Pages 10-38

    3. Bifurcations of Limit Cycles

      • V. I. Arnol’d
      Pages 38-79

    4. Nonlocal Bifurcations

      • V. I. Arnol’d
      Pages 79-153

    5. Relaxation Oscillations

      • V. I. Arnol’d
      Pages 154-205

  3. Catastrophe Theory

    1. Front Matter

      Pages 207-208
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    2. Basic Concepts

      • V. I. Arnol’d
      Pages 207-215

    3. The Theory of Catastrophes Before Poincaré

      • V. I. Arnol’d
      Pages 215-220

    4. The Theory of Bifurcations in the Work of Poincaré

      • V. I. Arnol’d
      Pages 220-224

    5. The Theory of Bifurcations in the Work of A.A. Andronov

      • V. I. Arnol’d
      Pages 224-232

    6. Physicists’ Treatment of Catastrophes Before Catastrophe Theory

      • V. I. Arnol’d
      Pages 232-238

    7. Thom’s Conjecture

      • V. I. Arnol’d
      Pages 239-244

    8. Classifications of Singularities and Catastrophes

      • V. I. Arnol’d
      Pages 244-259

  4. Back Matter

    Pages 259-274
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Keywords

About this book

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Editors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    V. I. Arnol’d

Bibliographic Information

  • Book Title: Dynamical Systems V

  • Book Subtitle: Bifurcation Theory and Catastrophe Theory

  • Editors: V. I. Arnol’d

  • DOI: https://doi.org/10.1007/978-3-642-57884-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Hardcover ISBN: 978-3-540-18173-6Published: 06 June 1994

  • Softcover ISBN: 978-3-540-65379-0Published: 20 May 1999

  • eBook ISBN: 978-3-642-57884-7Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: IX, 274

  • Additional Information: Original Russian edition published by Vinitii, Moscow, 1986 Originally published as Volume 5 in the Series:Encyclopaedia of Mathematical Sciences.

  • Topics: Analysis, Complex Systems, Statistical Physics and Dynamical Systems

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