Algebraic Ideas In Ergodic Theory

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Algebraic Ideas In Ergodic Theory

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Author : Klaus Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Algebraic Ideas In Ergodic Theory written by Klaus Schmidt 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 1990 with Mathematics categories.

The author examines the influence of operator algebras on dynamics, concentrating on ergodic equivalence relations. He also covers higher dimensional Markov shifts, making the assumption that the Markov shift carries a group structure.

Algebraic Ideas In Ergodic Theory

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Author : Klaus Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date :

Algebraic Ideas In Ergodic Theory written by Klaus Schmidt 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 with Mathematics categories.

Ergodic Theory

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Author : David Kerr
language : en
Publisher: Springer
Release Date : 2017-02-09

Ergodic Theory written by David Kerr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-09 with Mathematics categories.

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Dynamical Systems Ergodic Theory And Applications

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Author : L.A. Bunimovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-05

Dynamical Systems Ergodic Theory And Applications written by L.A. Bunimovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Mathematics categories.

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 modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Ergodic Theory Via Joinings

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Author : Eli Glasner
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-01-09

Ergodic Theory Via Joinings written by Eli Glasner 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 2015-01-09 with Mathematics categories.

This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.

Topics In Ergodic Theory Pms 44 Volume 44

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Author : Iakov Grigorevich Sinai
language : en
Publisher: Princeton University Press
Release Date : 2017-03-14

Topics In Ergodic Theory Pms 44 Volume 44 written by Iakov Grigorevich Sinai and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-14 with Mathematics categories.

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Global Aspects Of Ergodic Group Actions

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Author : A. S. Kechris
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Global Aspects Of Ergodic Group Actions written by A. S. Kechris 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 2010 with Mathematics categories.

A study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces.

Introduction To The Modern Theory Of Dynamical Systems

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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 1995

Introduction To The Modern Theory Of Dynamical Systems written by Anatole Katok 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 1995 with Mathematics categories.

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Algebraic Analysis Of Solvable Lattice Models

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Author : Michio Jimbo
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Algebraic Analysis Of Solvable Lattice Models written by Michio Jimbo 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 1995 with Mathematics categories.

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.

Recurrence In Ergodic Theory And Combinatorial Number Theory

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Author : Harry Furstenberg
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14

Recurrence In Ergodic Theory And Combinatorial Number Theory written by Harry Furstenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.