Normally Hyperbolic Invariant Manifolds
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Normally Hyperbolic Invariant Manifolds
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Author : Jaap Eldering
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-17
Normally Hyperbolic Invariant Manifolds written by Jaap Eldering and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-17 with Mathematics categories.
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.
Normally Hyperbolic Invariant Manifolds In Dynamical Systems
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Author : Stephen Wiggins
language : en
Publisher:
Release Date : 1984
Normally Hyperbolic Invariant Manifolds In Dynamical Systems written by Stephen Wiggins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Normally Hyperbolic Invariant Manifolds In Dynamical Systems
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Author : Stephen Wiggins
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Normally Hyperbolic Invariant Manifolds In Dynamical Systems written by Stephen Wiggins and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.
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.
Invariant Manifolds
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Author : M.W. Hirsch
language : en
Publisher: Springer
Release Date : 2006-11-15
Invariant Manifolds written by M.W. Hirsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Continuation Of Invariant Manifolds
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Author : Guang Yang
language : en
Publisher:
Release Date : 2008
Continuation Of Invariant Manifolds written by Guang Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space
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Author : Peter W. Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space written by Peter W. Bates and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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
Invariant Manifolds And Fibrations For Perturbed Nonlinear Schr Dinger Equations
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Author : Charles Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Invariant Manifolds And Fibrations For Perturbed Nonlinear Schr Dinger Equations written by Charles Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.
The Parameterization Method For Invariant Manifolds
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Author : Àlex Haro
language : en
Publisher: Springer
Release Date : 2016-04-18
The Parameterization Method For Invariant Manifolds written by Àlex Haro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
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.
Smooth Invariant Manifolds And Normal Forms
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Author : Alexander Kopanskii
language : en
Publisher: World Scientific
Release Date : 1994-12-22
Smooth Invariant Manifolds And Normal Forms written by Alexander Kopanskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-22 with Science categories.
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.
Lectures On Invariant Manifolds Of Perturbed Differential Equations And Linearization
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Author : George Osipenko
language : en
Publisher:
Release Date : 1996
Lectures On Invariant Manifolds Of Perturbed Differential Equations And Linearization written by George Osipenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Differential equations categories.