Normally Hyperbolic Invariant Manifolds in Dynamical Systems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Normally Hyperbolic Invariant Manifolds in Dynamical Systems PDF full book. Access full book title Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins. Download full books in PDF and EPUB format.
Author: Stephen Wiggins Publisher: Springer Science & Business Media ISBN: 1461243122 Category : Mathematics Languages : en Pages : 198
Book Description
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: Stephen Wiggins Publisher: Springer Science & Business Media ISBN: 1461243122 Category : Mathematics Languages : en Pages : 198
Book Description
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: Àlex Haro Publisher: Springer ISBN: 3319296620 Category : Mathematics Languages : en Pages : 280
Book Description
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: Jaap Eldering Publisher: Springer Science & Business Media ISBN: 9462390037 Category : Mathematics Languages : en Pages : 197
Book Description
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: H.W. Broer Publisher: Birkhäuser ISBN: 3034875185 Category : Mathematics Languages : en Pages : 464
Book Description
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.
Author: Bernd Aulbach Publisher: World Scientific ISBN: 9789810225483 Category : Mathematics Languages : en Pages : 332
Book Description
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.
Author: Eusebius Doedel Publisher: World Scientific ISBN: 9814478989 Category : Science Languages : en Pages : 357
Book Description
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.
Author: Alexander N. Gorban Publisher: Springer Science & Business Media ISBN: 3540358889 Category : Science Languages : en Pages : 554
Book Description
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.
Author: J.A. Tenreiro Machado Publisher: Springer Science & Business Media ISBN: 9048198844 Category : Technology & Engineering Languages : en Pages : 411
Book Description
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
Author: Stephen Wiggins Publisher: Springer Science & Business Media ISBN: 0387217495 Category : Mathematics Languages : en Pages : 860
Book Description
This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Author: Stephen Wiggins
Author: Stephen Wiggins
Author: Àlex Haro
Author: M.W. Hirsch
Author: Jaap Eldering
Author: H.W. Broer
Author: Bernd Aulbach
Author: Eusebius Doedel
Author: Alexander N. Gorban
Author: J.A. Tenreiro Machado
Author: Stephen Wiggins