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Ergodic theory, randomness, and dynamical systems by Donald Ornstein

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Published by Yale University Press in New Haven .
Written in English


  • Ergodic theory.,
  • Transformations (Mathematics),
  • Isomorphisms (Mathematics),
  • Stochastic processes.

Book details:

Edition Notes

Includes bibliographical references.

Statementby Donald S. Ornstein.
SeriesJames K. Whittemore lectures in mathematics given at Yale University, Yale mathematical monographs ;, 5
LC ClassificationsQA313 .O76
The Physical Object
Paginationvii, 141 p. ;
Number of Pages141
ID Numbers
Open LibraryOL5441182M
ISBN 100300017456
LC Control Number73090903

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Randomness and Recurrence in Dynamical Systems. discusses a wide range of topics such as irrational numbers, dynamical systems, normal numbers, ergodic theory, Benford's law, and (of course) infinitely many monkeys typing out Hamlet, all expertly woven together in a cohesive whole.. The first 40 or so pages of the book, including the table of contents, can be previewed Cited by: 1. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.   Ergodic theory is the bit of mathematics that concerns itself with studying the evolution of a dynamic system. Ergodicity involves taking into account the past and future, to get an appreciation of the distributive functions of a system. I know th. Get this from a library! Ergodic theory, randomness, and dynamical systems. [Donald Ornstein].

“This page book covers most relevant topics for a course in ergodic theory and dynamical systems, addressing topological and measure theoretic perspectives, and including notions of entropy. The subjects are illustrated with selected examples and bibliographical notes on the development of the theory. This book is the first systematic presentation of the theory of random dynamical systems, i.e. of dynamical systems under the influence of some kind of randomness. The theory comprises products of random mappings as well as random and stochastic differential equations. The author's approach is based on Oseledets'multiplicative ergodic theorem. By Donald S. Ornstein: pp. vii, £ (soft cover). (Yale University Press, )Author: R. K. Thomas. Although piecewise isometries (PWIs) are higher-dimensional generalizations of one-dimensional interval exchange transformations (IETs), their generic dynamical properties seem to be quite different. In this paper, we consider embeddings of IET dynamics into PWI with a view to better understanding their similarities and differences.

Ergodic Theory and Dynamical Systems is a peer-reviewed mathematics journal published by Cambridge University Press. Established in , the journal publishes articles on dynamical systems. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its impact factor was Discipline: Dynamical systems. An Introduction to Ergodic Theory (Graduate Texts in Mathematics) by Peter Walters. Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen. Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) by Anatole Katok and Boris Hasselblatt. regarding his hypothesis: for large systems of interacting particles in equilib-rium, the time average along a single trajectory equals the space average. The hypothesis as it was stated was false, and the investigation for the conditions under which these two quantities are equal lead to the birth of ergodic theory as is known nowadays.   The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra/5(2).