Normally Hyperbolic Invariant Manifolds In Dynamical Systems
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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.
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
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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.
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.
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.
Six Lectures On Dynamical Systems
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Author : Bernd Aulbach
language : en
Publisher: World Scientific
Release Date : 1996-05-15
Six Lectures On Dynamical Systems written by Bernd Aulbach and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with Mathematics categories.
This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Multiple Time Scale Dynamical Systems
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Author : Christopher K.R.T. Jones
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiple Time Scale Dynamical Systems written by Christopher K.R.T. Jones 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.
Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
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