Lyapunov Exponents And Smooth Ergodic Theory
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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.
Lyapunov Exponents And Smooth Ergodic Theory
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Author : Luis Barreira
language : en
Publisher:
Release Date : 2020
Lyapunov Exponents And Smooth Ergodic Theory written by Luis Barreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Ergodic theory categories.
Introduction To Smooth Ergodic Theory
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Author : Luís Barreira
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-28
Introduction To Smooth Ergodic Theory written by Luís Barreira and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-28 with Mathematics categories.
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.
Smooth Ergodic Theory For Endomorphisms
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Author : Min Qian
language : en
Publisher: Springer
Release Date : 2009-07-07
Smooth Ergodic Theory For Endomorphisms written by Min Qian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-07 with Mathematics categories.
Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.
Smooth Ergodic Theory For Endomorphisms
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Author : Min Qian
language : en
Publisher:
Release Date : 2009
Smooth Ergodic Theory For Endomorphisms written by Min Qian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Differentiable dynamical systems categories.
This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin's entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X.
Smooth Ergodic Theory Of Random Dynamical Systems
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Author : Pei-Dong Liu
language : en
Publisher: Springer
Release Date : 2006-11-14
Smooth Ergodic Theory Of Random Dynamical Systems written by Pei-Dong Liu 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.
This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.
Nonuniform Hyperbolicity
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Author : Luis Barreira
language : en
Publisher:
Release Date : 2014-02-19
Nonuniform Hyperbolicity written by Luis Barreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-19 with categories.
A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.
Smooth Ergodic Theory And Its Applications
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Author : A. B. Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Smooth Ergodic Theory And Its Applications written by A. B. Katok 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 2001 with Mathematics categories.
During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.
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.
Lyapunov Exponents
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Author : Luís Barreira
language : en
Publisher: Birkhäuser
Release Date : 2019-06-06
Lyapunov Exponents written by Luís Barreira and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-06 with Mathematics 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.