Bifurcation Theory and Catastrophe Theory
(Sprache: Englisch)
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...
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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, previouslypublished as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Inhaltsverzeichnis zu „Bifurcation Theory and Catastrophe Theory “
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 Poincaré.
3. The Theory of Bifurcations in the Work of Poincaré.
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.
Bibliographische Angaben
- Autoren: V.I. Arnold , V.S. Afrajmovich , Yu.S. Il'yashenko
- 1999, Softcover reprint of the original 1st ed. 1994., 274 Seiten, 130 Abbildungen, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Herausgegeben:Arnold, V.I.;Übersetzung:Kazarinoff, N.
- Verlag: Springer
- ISBN-10: 3540653791
- ISBN-13: 9783540653790
Sprache:
Englisch
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