Smooth ergodic theory and its applications : proceedings of the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications, July 26-August 13, 1999, University of Washington, Seattle / Anatole Katok [and three others], editors.

Format:

Book

Conference/Event

Contributor:

Katok, A. B., editor.

Conference Name:

AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (1999 : University of Washington), issuing body.

Series:

Proceedings of symposia in pure mathematics ; volume 69.

Proceedings of symposia in pure mathematics, 0082-0717 ; volume 69

Language:

English

Subjects (All):

Ergodic theory--Congresses.

Ergodic theory.

Physical Description:

1 online resource (894 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

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.

Contents:

""Statistical properties of some almost hyperbolic systems""""Random f-expansions""; ""Dynamical zeta functions""; ""An overview of the dimension theory of dynamical systems""; ""Collet-Eckmann condition in one-dimensional dynamics""; ""Monotonicity, J-algebra of Potapov and Lyapunov exponents""; ""Part lIb: Geodesic Flows""; ""Geodesic flows in manifolds of nonpositive curvature""; ""Closed geodesies and the uniqueness of the maximal measure for rank 1 geodesic flows""; ""Part llc: Algebraic Systems and Rigidity""; ""Invariant measures for actions of higher rank abelian groups""

""Some applications of homogeneous dynamics to number theory""""Measurable rigidity of algebraic Z[sup(d)]-actions""; ""Part lld: KAM-theory""; ""Almost reducibility of linear quasi-periodic systems""; ""A lecture on the classical KAM theorem""; ""A Lagrangian proof of the invariant curve theorem for twist mappings""; ""Part III. Research Articles""; ""Thermodynamical formalism for piecewise invertible maps: Absolutely continuous invariant measures as equilibrium states""; ""Smoothness of holonomy maps derived from unstable foliation""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-9374-2