Normally Hyperbolic Invariant Manifolds

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
ISBN 13 : 1461243122
Total Pages : 198 pages
Book Rating : 4.20/5 ( download)

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Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
ISBN 13 : 9780387942056
Total Pages : 212 pages
Book Rating : 4.5X/5 ( download)

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Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 1994-06-10 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Stephen Wiggins
Publisher : Springer
ISBN 13 : 9781461243137
Total Pages : 194 pages
Book Rating : 4.30/5 ( download)

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Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer. This book was released on 2013-12-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jaap Eldering
Publisher : Springer Science & Business Media
ISBN 13 : 9462390037
Total Pages : 197 pages
Book Rating : 4.34/5 ( download)

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Download or read book Normally Hyperbolic Invariant Manifolds written by Jaap Eldering and published by Springer Science & Business Media. This book was released on 2013-08-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context. Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds.

Author : Stephen Wiggins
Publisher :
ISBN 13 :
Total Pages : 193 pages
Book Rating : 4.67/5 ( download)

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Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by . This book was released on 1984 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M.W. Hirsch
Publisher : Springer
ISBN 13 : 3540373829
Total Pages : 153 pages
Book Rating : 4.27/5 ( download)

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Download or read book Invariant Manifolds written by M.W. Hirsch and published by Springer. This book was released on 2006-11-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Àlex Haro
Publisher : Springer
ISBN 13 : 3319296620
Total Pages : 267 pages
Book Rating : 4.23/5 ( download)

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Download or read book The Parameterization Method for Invariant Manifolds written by Àlex Haro and published by Springer. This book was released on 2016-04-18 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.

Author : Guang Yang
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.64/5 ( download)

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Download or read book Continuation of Invariant Manifolds written by Guang Yang and published by . This book was released on 2008 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander Kopanskii
Publisher : World Scientific
ISBN 13 : 9814502642
Total Pages : 398 pages
Book Rating : 4.41/5 ( download)

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Download or read book Smooth Invariant Manifolds And Normal Forms written by Alexander Kopanskii and published by World Scientific. This book was released on 1994-12-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.

Author : Peter W. Bates
Publisher : American Mathematical Soc.
ISBN 13 : 0821808680
Total Pages : 145 pages
Book Rating : 4.89/5 ( download)

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Download or read book Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space written by Peter W. Bates and published by American Mathematical Soc.. This book was released on 1998 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR