Titlebook: Dynamical Systems V; Bifurcation Theory a V. I. Arnol’d Book 1994 Springer-Verlag Berlin Heidelberg 1994 Bifurcation Theory.Bifurkationsthe

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Herz, Kreislauf und H?modynamik them”, said Poincaré (., Part 2, Chapter V (Analysis and physics), p. 222 (1905b)). In 1931, following this prescription, A.A. Andronov (1933) came out with a vast program (also set forth in the preface to Andronov and Khajkin, 1937) which differs from the contemporary program of catastrophe theori

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Verst?ndlichkeit ist nur der Anfangnt the entire space of objects studied as a finite union of submanifolds of codimensions not greater than . (called .) and a remainder of codimension ?. + 1 so that within each class an object’s properties that are of interest to us do not change. Then all objects in typical, no more than .-paramete

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ius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.978-3-540-65379-0978-3-642-57884-7

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Bifurcations of Equilibriaparameters are changed continuously and smoothly. Thus, upon loss of stability, a limit cycle may arise from a singular point, and the loss of stability by a limit cycle may give rise to chaos. Such changes are termed bifurcations.

宏偉

Bifurcations of Limit Cycles. Therefore the basic objects of study in this chapter are the bifurcations of germs of diffeomorphisms at a fixed point. Local families of germs of diffeomorphisms, their equivalence and weak equivalence, and induced and versal deformations of such germs are defined just as for germs of vector fiel

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