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Titlebook: Normally Hyperbolic Invariant Manifolds in Dynamical Systems; Stephen Wiggins Textbook 1994 Springer Science+Business Media New York 1994

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書目名稱Normally Hyperbolic Invariant Manifolds in Dynamical Systems
編輯Stephen Wiggins
視頻videohttp://file.papertrans.cn/669/668078/668078.mp4
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Normally Hyperbolic Invariant Manifolds in Dynamical Systems;  Stephen Wiggins Textbook 1994 Springer Science+Business Media New York 1994
描述In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.
出版日期Textbook 1994
關(guān)鍵詞dynamical systems; dynamics; manifold
版次1
doihttps://doi.org/10.1007/978-1-4612-4312-0
isbn_softcover978-1-4612-8734-6
isbn_ebook978-1-4612-4312-0Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 1994
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沙發(fā)
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0066-5452 rtant tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscill
地板
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The Unstable Manifold of an Overflowing Invariant Manifold,he unstable manifold of .. Afterward, we will show that this unstable manifold also satisfies the hypotheses of the persistence theorem for overflowing invariant manifolds. Hence, . will also have an unstable manifold under appropriate hypotheses. We begin developing the setting in much the same way as earlier.
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https://doi.org/10.1007/978-1-4612-4312-0dynamical systems; dynamics; manifold
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Examples,In this chapter we collect together several examples that illustrate the use and range of the theory developed in the previous chapters.
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