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Author | : Stephen Wiggins |
Publisher | : Springer Science & Business Media |
Total Pages | : 198 |
Release | : 2013-11-22 |
Genre | : Mathematics |
ISBN | : 1461243122 |
Download Normally Hyperbolic Invariant Manifolds in Dynamical Systems Book in PDF, ePub and Kindle
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 |
Total Pages | : 197 |
Release | : 2013-08-17 |
Genre | : Mathematics |
ISBN | : 9462390037 |
Download Normally Hyperbolic Invariant Manifolds Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 193 |
Release | : 1984 |
Genre | : |
ISBN | : |
Download Normally Hyperbolic Invariant Manifolds in Dynamical Systems Book in PDF, ePub and Kindle
Author | : M.W. Hirsch |
Publisher | : Springer |
Total Pages | : 153 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540373829 |
Download Invariant Manifolds Book in PDF, ePub and Kindle
Author | : Marta Canadell |
Publisher | : |
Total Pages | : 0 |
Release | : 2014 |
Genre | : |
ISBN | : |
Download Computation of Normally Hyperbolic Invariant Manifolds Book in PDF, ePub and Kindle
Author | : Marta Canadell Cano |
Publisher | : |
Total Pages | : 207 |
Release | : 2014 |
Genre | : |
ISBN | : |
Download Computation of Normally Hyperbolic Invariant Manifolds Book in PDF, ePub and Kindle
Author | : Àlex Haro |
Publisher | : Springer |
Total Pages | : 280 |
Release | : 2016-04-18 |
Genre | : Mathematics |
ISBN | : 3319296620 |
Download The Parameterization Method for Invariant Manifolds Book in PDF, ePub and Kindle
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 | : H. W. Broer |
Publisher | : |
Total Pages | : 37 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download Algorithms for Computing Normally Hyperbolic Invariant Manifolds Book in PDF, ePub and Kindle
Author | : Guang Yang |
Publisher | : |
Total Pages | : 192 |
Release | : 2008 |
Genre | : |
ISBN | : |
Download Continuation of Invariant Manifolds Book in PDF, ePub and Kindle
Author | : J. Eldering |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Persistence of Noncompact Normally Hyperbolic Invariant Manifolds in Bounded Geometry Book in PDF, ePub and Kindle