О книге

Арнольд Владимир Игоревич - Теория катастроф

Издание третье, дополненное

Москва "Наука" главная редакция физико-математической литературы 1990

ББК 22.16

А84 УДК 517(023)

Арнольд В. И. Теория катастроф. - 3-е изд., доп. - М.: Наука. Гл. ред. физ.-мат. лит., 1990. - С. 128. - ISBN 5-02-014271-9

Ил. 87. Библиогр. 176 назв.

Рецензент доктор физико-математических наук А. В. Чернавский

Научно-популярное издание Заведующий редакцией А. П. Баева

Редактор В. В. Абгарян

Художественный редактор Г. М. Коровина

Технический редактор А. П. Колесникова

Корректоры Т. Г. Егорова, В. П. Сорокина ИБ № 32891

Сдано в набор 06.06.89. Подписано к печати 21.03.90. Формат 84х108¹/₃₂. Бумага тип. № 2. Гарнитура обыкновенная. Печать высокая. Усл. печ, п. 6,72. Усл. кр.-отт. 6,93. Уч.-изд. л. 7,3. Тираж 84000 экз. Заказ № 3647.

Издательско-производственное и книготорговое объединение "Наука" Главная редакция физико-математической литературы 117071 Москва В-71, Ленинский проспект, 15

Вторая типография ИПКО "Наука" 121099 Москва Г-99, Шубинский пер., 6

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, the 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, perestroikas 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 both 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 - Volterra 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.