Catastrophe TheorySpringer-Verlag, 1992 - 150 pages 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 |
Table des matières
Singularities Bifurcations and Catastrophes | 1 |
Whitneys Singularity Theory | 3 |
Applications of Whitneys Theory | 7 |
Droits d'auteur | |
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Expressions et termes fréquents
Anal Appl attractor bifurcation catastrophe theory caustics and wave classification codimension complex contact structure convex hulls coordinates critical points critical values cusp points cusp ridge diffeomorphic dimension Dynamical Systems E. C. Zeeman English translation equation equilibrium Euclidean space example Funct Funkts Gauss mapping geodesics geometry hypersurface indicatrix inflection intersection investigation Itogi Nauki Tekh Lagrangian Legendre Let us consider level curve level manifold limiting curves loss of stability mapping Math mathematical metamorphoses monodromy Moscow Nauk neighbourhood normal form obstacle surface one-parameter family oscillations parameter phase curves phase space plane Poincaré polynomials Prilozh problem projection Russ Russian Shcherbak singu singular points singularities of caustics singularity theory small perturbation smooth surfaces Sovrem sphere submanifold Surv swallowtail symplectic structure tangent theorem Thom three-dimensional space three-space tion topologically torus transformation typical singularities V. I. Arnol'd vanishing cycle variables vector field velocity VINITI visible contour wave fronts Whitney's zero