V.S. Afrajmovich's Books

Dynamical Systems V

Bifurcation Theory and Catastrophe Theory

By: V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov

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Dynamical Systems V

Bifurcation Theory and Catastrophe Theory

By: V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" 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.

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Page Count

279

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642578845

ISBN 13

9783642578847

Multidimensional Strange Attractors and Turbulence

By: I. S. Aranson,Mikhail Izrailevich Rabinovich,M. I. Rabinovich,V. S. Afraimovich

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Multidimensional Strange Attractors and Turbulence

By: I. S. Aranson,Mikhail Izrailevich Rabinovich,M. I. Rabinovich,V. S. Afraimovich

The authors explore the origin of multidimensional strange attractors and their role in describing turbulence. It includes an analytical estimation of the deminsions of strange attractors for models described by differential-difference equations and discusses the conditions in which space-homogeneous chaos is stable with respect to random perturbations in flow systems.

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