Smooth Ergodic Theory and Its Applications

Smooth Ergodic Theory and Its Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 895
Release :
ISBN-10 : 9780821826829
ISBN-13 : 0821826824
Rating : 4/5 (824 Downloads)

Book Synopsis Smooth Ergodic Theory and Its Applications by : A. B. Katok

Download or read book Smooth Ergodic Theory and Its Applications written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2001 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Smooth Ergodic Theory and Its Applications Related Books

Smooth Ergodic Theory and Its Applications
Language: en
Pages: 895
Authors: A. B. Katok
Categories: Mathematics
Type: BOOK - Published: 2001 - Publisher: American Mathematical Soc.

GET EBOOK

During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mat
Introduction to Smooth Ergodic Theory
Language: en
Pages: 355
Authors: Luís Barreira
Categories: Mathematics
Type: BOOK - Published: 2023-05-19 - Publisher: American Mathematical Society

GET EBOOK

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
Dynamical Systems, Ergodic Theory and Applications
Language: en
Pages: 476
Authors: L.A. Bunimovich
Categories: Mathematics
Type: BOOK - Published: 2000-04-05 - Publisher: Springer Science & Business Media

GET EBOOK

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of mode
Lyapunov Exponents and Smooth Ergodic Theory
Language: en
Pages: 166
Authors: Luis Barreira
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: American Mathematical Soc.

GET EBOOK

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)
Introduction to Smooth Ergodic Theory
Language: en
Pages: 355
Authors: Luís Barreira
Categories: Mathematics
Type: BOOK - Published: 2023-04-28 - Publisher: American Mathematical Society

GET EBOOK

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