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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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書目名稱Dynamical Systems V
副標(biāo)題Bifurcation Theory a
編輯V. I. Arnol’d
視頻videohttp://file.papertrans.cn/284/283870/283870.mp4
概述The authors are masters in fields of bifurcation theory and catastrophe theory.Arnol‘d is known for keeping the mathematics correct and avoiding non-rigorous applications.Includes supplementary materi
圖書封面Titlebook: Dynamical Systems V; Bifurcation Theory a V. I. Arnol’d Book 1994 Springer-Verlag Berlin Heidelberg 1994 Bifurcation Theory.Bifurkationsthe
描述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.
出版日期Book 1994
關(guān)鍵詞Bifurcation Theory; Bifurkationstheorie; Catastrophe Theory; Dynamical Systems; Dynamische Systeme; Katas
版次1
doihttps://doi.org/10.1007/978-3-642-57884-7
isbn_softcover978-3-540-65379-0
isbn_ebook978-3-642-57884-7
copyrightSpringer-Verlag Berlin Heidelberg 1994
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The Theory of Catastrophes Before Poincaréed by Huygens.) Thus, Huygens essentially discovered the stability of cusps on caustics and wave fronts. Nowadays these singularities are connected with the pleats of the corresponding smooth mappings, and they belong to the most important applications of catostrope theory. Fig. 7 was discussed by Cayley (1868b).
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The Theory of Bifurcations in the Work of Poincaréscover of the normal form of a symplectic structure) created the general method of normal forms, which leads to the classification of catastrophes if one applies it to functions instead of to differential equations.
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Physicists’ Treatment of Catastrophes Before Catastrophe Theoryt calculations. (1974) in an article “Nobel prizes for catastrophes” points out many examples of acknowledged physical achievements, whose authors, independently of one another, used ideas formalized later in singularity theory.
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