Invariant Manifolds
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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.
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.
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 And Dispersive Hamiltonian Evolution Equations
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Author : Kenji Nakanishi
language : en
Publisher: European Mathematical Society
Release Date : 2011
Invariant Manifolds And Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Hamiltonian systems categories.
The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.
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 Differentiable dynamical systems 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.
Invariant Manifolds In Discrete And Continuous Dynamical Systems
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Author : Kaspar Nipp
language : en
Publisher:
Release Date : 2013
Invariant Manifolds In Discrete And Continuous Dynamical Systems written by Kaspar Nipp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
In this book, dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first part, discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part, analogous results for continuous dynamical systems in finite dimensions are established. In the third part, the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations. The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting that provides quantitative estimates. The book is targeted at researchers in the field of dynamical systems interested in precise theorems that are easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics.
Approximation Of Stochastic Invariant Manifolds
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Author : Mickaël D. Chekroun
language : en
Publisher: Springer
Release Date : 2014-12-20
Approximation Of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities
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Author : Anatole Katok
language : en
Publisher: Springer
Release Date : 2006-12-08
Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities written by Anatole Katok and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Invariant Manifolds
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Author :
language : en
Publisher:
Release Date : 1964
Invariant Manifolds written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Foliations (Mathematics) categories.