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Local Lyapunov Exponents

Author : Wolfgang Siegert

Publisher : Springer Science & Business Media

Page : 264 pages

File Size : 21,42 MB

Release : 2009

Category : Mathematics

ISBN : 3540859632

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Book Description

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.



Lectures on Lyapunov Exponents

Author : Marcelo Viana

Publisher : Cambridge University Press

Page : 217 pages

File Size : 21,30 MB

Release : 2014-07-24

Category : Mathematics

ISBN : 1316062694

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Book Description

The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.



Lyapunov Exponents

Author : Luís Barreira

Publisher : Birkhäuser

Page : 273 pages

File Size : 43,2 MB

Release : 2017-12-30

Category : Mathematics

ISBN : 3319712616

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Book Description

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.



Lyapunov Exponents

Author : Arkady Pikovsky

Publisher : Cambridge University Press

Page : 415 pages

File Size : 21,12 MB

Release : 2016-02-11

Category : Science

ISBN : 1316467708

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Book Description

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.



Lyapunov Exponents and Smooth Ergodic Theory

Author : Luis Barreira

Publisher : American Mathematical Soc.

Page : 166 pages

File Size : 42,64 MB

Release : 2002

Category : Mathematics

ISBN : 0821829211

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Book Description

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.



Random Dynamical Systems

Author : Ludwig Arnold

Publisher : Springer Science & Business Media

Page : 590 pages

File Size : 27,15 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 3662128780

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Book Description

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.



Lyapunov Exponents

Author : Ludwig Arnold

Publisher : Lecture Notes in Mathematics

Page : 392 pages

File Size : 19,84 MB

Release : 1986-03

Category : Mathematics

ISBN :

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Book Description

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.



Dynamical Systems with Applications using MATLAB®

Author : Stephen Lynch

Publisher : Springer Science & Business Media

Page : 504 pages

File Size : 33,87 MB

Release : 2004-06-10

Category : Technology & Engineering

ISBN : 9780817643218

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Book Description

This introduction to dynamical systems theory guides readers through theory via example and the graphical MATLAB interface; the SIMULINK® accessory is used to simulate real-world dynamical processes. Examples included are from mechanics, electrical circuits, economics, population dynamics, epidemiology, nonlinear optics, materials science and neural networks. The book contains over 330 illustrations, 300 examples, and exercises with solutions.



Nonuniform Hyperbolicity

Author : Luis Barreira

Publisher :

Page : pages

File Size : 48,51 MB

Release : 2014-02-19

Category :

ISBN : 9781299707306

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Book Description

A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.



Nonlinear Dynamics

Author : Muthusamy Lakshmanan

Publisher : Springer Science & Business Media

Page : 628 pages

File Size : 17,26 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 3642556884

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Book Description

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.