Pisa Lectures on Lyapunov Exponents
Author | : Marcelo Viana |
Publisher | : |
Total Pages | : 26 |
Release | : 2003 |
Genre | : |
ISBN | : |
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Author | : Marcelo Viana |
Publisher | : |
Total Pages | : 26 |
Release | : 2003 |
Genre | : |
ISBN | : |
Author | : Marcelo Viana |
Publisher | : Cambridge University Press |
Total Pages | : 217 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1316062694 |
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.
Author | : Marcelo Viana |
Publisher | : Cambridge University Press |
Total Pages | : 217 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1107081734 |
Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
Author | : Ludwig Arnold |
Publisher | : Springer |
Total Pages | : 372 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354046431X |
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.
Author | : Ludwig Arnold |
Publisher | : Springer |
Total Pages | : 380 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540397957 |
Author | : Luís Barreira |
Publisher | : |
Total Pages | : 273 |
Release | : 2017 |
Genre | : Dynamics |
ISBN | : 9783319712628 |
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.
Author | : Wolfgang Siegert |
Publisher | : Springer Science & Business Media |
Total Pages | : 264 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 3540859632 |
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.
Author | : Ludwig Arnold |
Publisher | : |
Total Pages | : 376 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662183502 |
Author | : Luis Barreira |
Publisher | : American Mathematical Soc. |
Total Pages | : 166 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829211 |
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.
Author | : Pedro Duarte |
Publisher | : Springer |
Total Pages | : 271 |
Release | : 2016-03-21 |
Genre | : Mathematics |
ISBN | : 9462391246 |
The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.