Bifurcation theory and catastrophe theory

Author(s)

• Arnolʹd, Vladimir Igorevich

Bibliographic Information

Bifurcation theory and catastrophe theory

V.I. Arnol'd (ed.)

（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 5 . Dynamical systems ; 5）

Springer-Verlag, c1994

• : us
• : gw

Other Title

Dinamicheskie sistemy

Note

Includes bibliography and indexes

"Title of the Russian edition: Itogi nauki i tekhniki, ... Vol.5, Dinamicheskie sistemy 5"--T.p. verso

Description and Table of Contents

Description

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.

Table of Contents

I. Bifurcation Theory by V.I.Arnol'd, V.S.Afrajmovich, Yu.S.Il'yashenko, L.P.Shil'nikov: Preface.- 1. Bifurcations of Equilibria.- 2. Bifurcations of Limit Cycles.- 3. Nonlocal Bifurcations.- 4. Relaxation Oscillations.- Recommended Literature.- References II. Catastrophe Theory by V.I.Arnol'd: 1. Basic Concepts.- 2. The Theory of Catastrophes Before Poincare.- 3. The Theory of Bifurcations in the Work of Poincare.- 4. The Theory of Bifurcations in the Work of A.A.Andronov.- 5. Physicists' Treatment of Catastrophes Before Catastrophe Theory.- 6. Thom's Conjecture.- 7. Classifications of Singularities and Catastrophes.- Recommended Literature.- References

by "Nielsen BookData"

Details

• NCID: BA22690336
• ISBN:
  • 0387181733
  • 3540181733
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Berlin ; New York ; Tokyo
• Pages/Volumes: 271 p.
• Size: 24 cm
• Classification:
  • LCC : QA805
  • DC19 : 531
  • NDC8 : 423.35
  • NDC8 : 423.1
  • NDC8 : 413.6
• Subject Headings:
  • LCSH : Mechanics, Analytic
  • LCSH : Celestial mechanics
• Parent Bibliography ID:
  • BA01321819