Abstract
The first information on catastrophe theory appeared in the western press about ten years ago. In magazines like “Newsweek” there were reports of a revolution in mathematics, comparable perhaps to Newton’s invention of the differential and integral calculus. It was claimed that the new science, catastrophe theory, was much more valuable to mankind than mathematical analysis: while Newtonian theory only considers smooth, continuous processes, catastrophe theory provides a universal method for the study of all jump transitions, discontinuities, and sudden qualitative changes. There appeared hundreds of scientific and popular science publications in which catastrophe theory was applied to such diverse targets as, for instance, the study of heart beat, geometrical and physical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology, and the theory of elementary particles. Among the published works on catastrophe theory are studies of the stability of ships, models for the activity of the brain and mental disorders, for prison uprisings, for the behaviour of investors on the stock exchange, for the influence of alcohol on drivers and for censorship policy with respect to erotic literature.
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Bibliographical Comments
Extensive bibliographies are contained in:
T. Poston, I. Stewart: Catastrophe theory and its applications. Pitman, London-San Francisco-Melbourne 1978, 491 p.
V. I. Arnol’d, S. M. Gusein-Zade, A. N. Varchenko: Singularities of differentiable maps. vol. I, Nauka, Moscow 1982, 304 p. (English translation: Birkhäuser, Boston 1985, 382 p.) vol. II, Nauka, Moscow 1984, 336 p. (English translation: Birkhäuser, Boston, to appear)
E. C. Zeeman, B. W. W.: 1981 Bibliography on catastrophe theory. Coventry, University of Warwick 1981, 73 p.
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© 1986 Springer-Verlag Berlin Heidelberg
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Arnold, V.I. (1986). Singularities, Bifurcations, and Catastrophes. In: Catastrophe Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96937-9_1
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