Теория катастроф - Арнольд В.И.
ISBN 5-02-014271-9
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К заключению
Саати Т. JI. Математические модели конфликтных ситуаций,— M.: Сов. радио, 1977.— С. 47—53. This short book provides a concise, nonmathematical review of the less controversial results in singularities, bifurcations and pe-restroikas theory. The author begins by describing the elements of the singularity theory of smooth mappings and of the bifurcation and stability loss theory of dynamical systems, and continue with chapters on the applications of the theory to topics such as wavefront propagation, tne distribution of matter with in the universe, the geometry of apparent contours of smooth surfaces, the theory of implicit differential equations, symplectic and contact structures topology of Riemann surfaces, optimisation and control, perestroi-kas difficulties.
This new edition is more coplete than the 1986 (Springer) English edition. The main new parts are an historical survey of the works of the predecessors of catastrophe theory and a list of about a hundred problems, containing botn the exercises, intented to help the reader to master the theory, and to provide him with the formulations of some more sophisticated results in singularity theory. Among the 15 new figures one finds the patterns of the generic singularities of implicit differential equations and of the perestroikas of the apparent contours of the generic surfaces, viewed from nongeneric points of view, the list of the shock waves metamorphoses and the singularity of the caustics of a generic surface with boundary. The recent results, discussed in this new edition, includes the Neistadt delayed dynamical bifurcations theory, the Zoladek theory of Lotka — Vol-terra bifurcation, the Davydov description of the sigularities of the slow motions in relaxation systems with two slow variables and the Hessin classification of local bifurcations in generic three — parameter families of gradient dynamical systems.
