## Catastrophe TheoryFrom The 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 "... 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 |

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### Contents

Singularities Bifurcations and Catastrophes | 1 |

Whitneys Singularity Theory | 3 |

Applications of Whitneys Theory | 7 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

Anal appear Appl applications asymptotic attainability bifurcation bifurcation theory boundary called catastrophe theory caustic Chapter classification complex continuous convex coordinates corresponding critical points critical values curve cusp cusp ridge cycle defined depending described diffeomorphic differential dimension direction domain Dynamical English translation equation equilibrium example field fold follows Funct function Funkts geometry given initial intersection jump Lagrangian Let us consider limiting loss of stability manifold mapping Math mathematical means medium metamorphoses Moscow motion moving Nauk neighbourhood normal objects obstacle obtained original oscillations parameter passes path perturbation phase space plane polynomials position Prilozh problem projection Prove Russian segment simple singular points singularity theory smooth space sphere structure surface swallowtail symplectic tangent Thom three-dimensional space tion topologically transformation turns typical University V. I. Arnold vanishing variables vector visible wave fronts zero