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Table of Contents

1 Singularities, Bifurcations, and Catastrophes.- 2 Whitney’s Singularity Theory.- 3 Applications of Whitney’s Theory.- 4 A Catastrophe Machine.- 5 Bifurcations of Equilibrium States.- 6 Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour.- 7 Singularities of the Stability Boundary and the Principle of the Fragility of Good Things.- 8 Caustics, Wave Fronts, and Their Metamorphoses.- 9 The Large-Scale Distribution of Matter in the Universe.- 10 Singularities in Optimization Problems: the Maximum function.- 11 Singularities of the Boundary of Attainability.- 12 Smooth Surfaces and Their Projections.- 13 The Problem of Bypassing an Obstacle.- 14 Symplectic and Contact Geometry.- 15 Complex Singularities.- 16 The Mysticism of Catastrophe Theory.- Appendix The Precursors of Catastrophe Theory.- Conclusion.- Problems.- References.

Reviews

"This short book, which is a translation from the Russian, provides a concise, non-mathematical review of the less controversial results in catastrophe theory. The author begins by describing the established results in the theory of singularities and bifurcation and continues with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams. ... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject." Physics Bulletin December 1984 "Vladimir Arnold is a giant among contemporary mathematicians, and one of the three who stand out in the creation and development of catastrophe theory. ..." The Times Higher Education Supplement 1 June 1984 "... This is a beautiful little book, popular mathematics at its best, a delight to read and unreservedly recommended to novice and expert alike. ..." Acta Applicandae Mathematicae Vol. 7, 1986 "... The book can be warmly recommended to everyone who is interested in singularity theory. It also gives interesting information for researchers working on the subject." Acta Scientiarum Mathematicarum 59, 1994 "... There is probably no one else in the world who could have written this book. It remains an engrossing summary of a vast body of work which is one of the major achievements of twentieth-century mathematics." Mathematical Reviews, Issue 93h "This unusual little paperback ... has the qualities we tend to associate with Russian expository mathematical writing: a highly personal style, imaginatevely presented examples, nontechnical language, sometimes puzzling asides, and de trop obersations taken from the world at large. ..." The Mathematical Intelligencer 18.1996.4