Lectures On Lyapunov Exponents
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Lectures On Lyapunov Exponents
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Author : Marcelo Viana
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24
Lectures On Lyapunov Exponents written by Marcelo Viana and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
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.
Lyapunov Exponents
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Author : Ludwig Arnold
language : en
Publisher: Springer
Release Date : 2006-11-14
Lyapunov Exponents written by Ludwig Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant measures for nonlinear stochastic differential equations.- Y. Kifer: Large deviationsfor random expanding maps.- P. Thieullen: Generalisation du theoreme de Pesin pour l' -entropie.- S.T. Ariaratnam, W.-C. Xie: Lyapunov exponents in stochastic structural mechanics.- F. Colonius, W. Kliemann: Lyapunov exponents of control flows.
Local Lyapunov Exponents
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Author : Wolfgang Siegert
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
Local Lyapunov Exponents written by Wolfgang Siegert 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 2009 with Mathematics categories.
Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
New Trends In Lyapunov Exponents
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Author : João Lopes Dias
language : en
Publisher: Springer Nature
Release Date : 2023-11-29
New Trends In Lyapunov Exponents written by João Lopes Dias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-29 with Mathematics categories.
This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics. Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems. This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.
Lectures On Chaotic Dynamical Systems
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Author : Valentin Senderovich Afraĭmovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Lectures On Chaotic Dynamical Systems written by Valentin Senderovich Afraĭmovich 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 2003 with Chaotic behavior in systems categories.
Basic concepts Zero-dimensional dynamics One-dimensional dynamics Two-dimensional dynamics Systems with 1.5 degrees of freedom Systems generated by three-dimensional vector fields Lyapunov exponents Appendix Bibliography Index.
Lyapunov Exponents And Smooth Ergodic Theory
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Author : Luis Barreira
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Lyapunov Exponents And Smooth Ergodic Theory written by Luis Barreira 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 2002 with Mathematics categories.
A systematic introduction to the core of smooth ergodic theory. An expanded version of an earlier work by the same authors, it describes the general (abstract) theory of Lyapunov exponents and the theory's applications to the stability theory of differential equations, the stable manifold theory, absolute continuity of stable manifolds, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). It could be used as a primary text for a course on nonuniform hyperbolic theory or as supplemental reading for a course on dynamical systems. Assumes a basic knowledge of real analysis, measure theory, differential equations, and topology. c. Book News Inc.
Chaos Detection And Predictability
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Author : Charalampos (Haris) Skokos
language : en
Publisher: Springer
Release Date : 2016-03-04
Chaos Detection And Predictability written by Charalampos (Haris) Skokos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-04 with Science categories.
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.
Lyapunov Exponents
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Author : Luís Barreira
language : en
Publisher:
Release Date : 2017
Lyapunov Exponents written by Luís Barreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Dynamics categories.
This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
Collected Lectures On The Preservation Of Stability Under Discretization
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Author : Donald J. Estep
language : en
Publisher: SIAM
Release Date : 2002-01-01
Collected Lectures On The Preservation Of Stability Under Discretization written by Donald J. Estep and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
The 13 lectures are intended to be accessible to new graduate students of mathematics, sacrificing some detail in order to offer an accessible introduction to the fundamentals of stability that can provide a foundation for further study. Presenters from the US and Britain cover preserving qualitative stability features and structural stability, and investigating physical stability and model stability. Annotation copyrighted by Book News, Inc., Portland, OR