Computation Of Normally Hyperbolic Invariant Manifolds

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Computation Of Normally Hyperbolic Invariant Manifolds

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Author : Marta Canadell
language : en
Publisher:
Release Date : 2014

Computation Of Normally Hyperbolic Invariant Manifolds written by Marta Canadell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

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.

Computation Of Normally Hyperbolic Invariant Manifolds

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Author : Marta Canadell Cano
language : en
Publisher:
Release Date : 2014

Computation Of Normally Hyperbolic Invariant Manifolds written by Marta Canadell Cano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 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.

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.

Nonlinear Dynamical Systems And Chaos

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Author : H.W. Broer
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Nonlinear Dynamical Systems And Chaos written by H.W. Broer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann

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Author : Eusebius Doedel
language : en
Publisher: World Scientific
Release Date : 2006-03-10

Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann written by Eusebius Doedel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-10 with Science categories.

The Hungarian born mathematical genius, John von Neumann, was undoubtedly one of the greatest and most influential scientific minds of the 20th century. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J E Marsden, P J Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this book offers a unique combination of theoretical and applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics.The contents of this book was also published as a special issue of the International Journal of Bifurcation and Chaos — March 2005.

Model Reduction And Coarse Graining Approaches For Multiscale Phenomena

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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-22

Model Reduction And Coarse Graining Approaches For Multiscale Phenomena written by Alexander N. Gorban 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 2006-09-22 with Science categories.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

Nonlinear Science And Complexity

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Author : J.A. Tenreiro Machado
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03

Nonlinear Science And Complexity written by J.A. Tenreiro Machado 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 2010-11-03 with Science categories.

This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include • Chaotic Dynamics and Transport in Classic and Quantum Systems • Complexity and Nonlinearity in Molecular Dynamics and Nano-Science • Complexity and Fractals in Nonlinear Biological Physics and Social Systems • Lie Group Analysis and Applications in Nonlinear Science • Nonlinear Hydrodynamics and Turbulence • Bifurcation and Stability in Nonlinear Dynamic Systems • Nonlinear Oscillations and Control with Applications • Celestial Physics and Deep Space Exploration • Nonlinear Mechanics and Nonlinear Structural Dynamics • Non-smooth Systems and Hybrid Systems • Fractional dynamical systems