Bifurcation theory and catastrophe theory

著者

• Arnolʹd, Vladimir Igorevich

書誌事項

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

タイトル別名

Dinamicheskie sistemy

注記

Includes bibliography and indexes

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

内容説明・目次

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA22690336
• ISBN:
  • 0387181733
  • 3540181733
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 原本言語コード: rus
• 出版地: Berlin ; New York ; Tokyo
• ページ数/冊数: 271 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA805
  • DC19 : 531
  • NDC8 : 423.35
  • NDC8 : 423.1
  • NDC8 : 413.6
• 件名:
  • LCSH : Mechanics, Analytic
  • LCSH : Celestial mechanics
• 親書誌ID:
  • BA01321819