Author: P. Walters
Publisher:
ISBN: 3662166674
Category:
Page: 212
View: 528
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.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
Ergodic Theory
Introductory Lectures on 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.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.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
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.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.