Author | Arnold, Vladimir I. author |
---|---|

Title | Catastrophe Theory [electronic resource] / by Vladimir I. Arnold |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992 |

Edition | Third, Revised and Expanded Edition |

Connect to | http://dx.doi.org/10.1007/978-3-642-58124-3 |

Descript | XIII, 150 p. online resource |

SUMMARY

From 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

CONTENT

1 Singularities, Bifurcations, and Catastrophes -- 2 Whitneyโ{128}{153}s Singularity Theory -- 3 Applications of Whitneyโ{128}{153}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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Topology
Physics
Mathematics
Analysis
Topology
Theoretical Mathematical and Computational Physics