An Introduction to Ergodic Theory

An Introduction to Ergodic Theory

Preface In 1970 I gave a graduate course in ergodic theory at the University of Maryland in College Park , and these lectures were the basis of the Springer Lecture Notes in Mathematics Volume 458 called " Ergodic Theory- Introductory ...

Author: Peter Walters

Publisher: Springer Science & Business Media

ISBN: 0387951520

Category: Mathematics

Page: 268

View: 992

The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.
Categories: Mathematics

Ergodic Theory Introductory Lectures

Ergodic Theory     Introductory Lectures

The Ergodic. Theorem The first major result in ergodic theory was proved in 1931 by G. D. Birkhoff [l]. Theorem l. 5: (Birkhoff Ergodic Theorem) Suppose T: (X, B, m) → (X, B, m) is measure-preserving (where we l 1 * ...i allow (X, 8, ...

Author: P. Walters

Publisher: Springer

ISBN: 9783540374947

Category: Mathematics

Page: 203

View: 105

Categories: Mathematics

Ergodic Theory

Ergodic Theory

(1932d) Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. 33, 587–642. (1934) Almost periodic functions in a group, I, Trans, Amer. Math. Soc. 36, 445–92, WALTERS, PETER *(1975) Ergodic Theory: Introductory Lectures, ...

Author: Karl E. Petersen

Publisher: Cambridge University Press

ISBN: 9781316583203

Category: Mathematics

Page:

View: 283

The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.
Categories: Mathematics

Introduction to Ergodic Theory

Introduction to Ergodic Theory

... in - Publication Data Sinal , fakov Grigor ' evich , 1935- Introduction to ergodic theory . ( Mathematical notes ; 18 ) Based on a series of lectures given at the Moscow and Erevan State Universities . 1. Ergodic theory . I. Title .

Author: Iakov Grigorevich Sinai

Publisher: Princeton University Press

ISBN: 0691081824

Category: Mathematics

Page: 156

View: 881

Based on lectures in Erevan, this exposition of ergodic theory contains a rich collection of examples well chosen to introduce the reader to the main themes of the subject. Topics discussed include existence of invariant measures, geodesic flows on Riemannian manifolds, ergodic theory of an ideal gas, and entropy of dynamical systems.
Categories: Mathematics

Ergodic Theory and Statistical Mechanics

Ergodic Theory and Statistical Mechanics

Amer. J. of Math. 97 (1975), 937-971. WALTERS, P., Ergodic theory, introductory lectures. Lecture Notes in Mathematics 458, Springer-Verlag, Berlin, Heidelberg, New-York (1975). WALTERS, P., An Introduction to Ergodic Theory.

Author: Jean Moulin Ollagnier

Publisher: Springer

ISBN: 9783540392897

Category: Mathematics

Page: 152

View: 805

Categories: Mathematics

Topics in Ergodic Theory

Topics in Ergodic Theory

Proc . Nat . Acad . Sci . U.S.A. 18 ( 1932 ) , 263-6 . von Neumann , J. [ 3 ] . Zur Operatoren methode in der klassischen mechanik . Ann . Math . 33 ( 1932 ) , 587-642 . Walters , P. [ 1 ] . Ergodic theory - introductory lectures .

Author: William Parry

Publisher: Cambridge University Press

ISBN: 0521604907

Category: Mathematics

Page: 128

View: 306

An introduction to topics and examples of ergodic theory, a central area of pure mathematics.
Categories: Mathematics

Topics in Ergodic Theory PMS 44 Volume 44

Topics in Ergodic Theory  PMS 44   Volume 44

P. Billingsley, Ergodic Theory and Information. J. Wiley, 1965, 106p. 4. P. Walters, Ergodic Theory. Introductory Lectures. Lecture Notes in Mathematics No. 458, Springer-Verlag, 1975. 5. I. P. Cornfeld, S. V. Fomin, Ya.

Author: Iakov Grigorevich Sinai

Publisher: Princeton University Press

ISBN: 9781400887255

Category: Mathematics

Page: 226

View: 465

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.
Categories: Mathematics