Bifurcation theory and catastrophe theory

V.I. Arnold ... [et al.]

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.

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[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

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この本の情報

書名 Bifurcation theory and catastrophe theory
著作者等 Arnolʹd, Vladimir Igorevich
Arnold V. I.
Ilyashenko Yu.S
Kazarinoff N.D.
Shil'nikov L.P.
Afrajmovich V.S.
書名別名 Itogi nauki i tekhniki, sovremennye problemy matematiki
出版元 Springer-Verlag
刊行年月 c1999
ページ数 271 p.
大きさ 24 cm
ISBN 3540653791
NCID BA42306769
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言語 英語
原文言語 ロシア語
出版国 ドイツ
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