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Ergodic theory

Petersen, Karl Endel, (1943-)

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Ergodic theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ergodic theory/ Karl Petersen.
作者:	Petersen, Karl Endel,
出版者:	Cambridge :Cambridge University Press, : 1989.,
面頁冊數:	xi, 329 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Ergodic theory. -
電子資源:	https://doi.org/10.1017/CBO9780511608728
ISBN:	9780511608728

Ergodic theory
Petersen, Karl Endel,1943-

Ergodic theory[electronic resource] /Karl Petersen. - Cambridge :Cambridge University Press,1989. - xi, 329 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;2. - Cambridge studies in advanced mathematics ;2..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511608728Subjects--Topical Terms:

555691
Ergodic theory.

LC Class. No.: QA313 / .P47 1989

Dewey Class. No.: 515.42

Ergodic theory
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