COMBINATORIAL CONSTRUCTIONS IN ERGODIC THEORY AND DYNAMICS by Anatole Katok ( 9780821834961 )

Item Details

Title:

COMBINATORIAL CONSTRUCTIONS IN ERGODIC THEORY AND DYNAMICS

By:

Anatole Katok

Format:

Paperback

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£61.00

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£54.90

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ISBN 10:

0821834967

ISBN 13:

9780821834961

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Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 October, 2003

Series:

University Lecture Series No. 30

Pages:

121

Description:

Explores genericity of approximation in various categories and presents many applications, including spectral multiplicity and properties of the maximal spectral type. This book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining asymptotic behavior from approximate pictures at different time scales.

Synopsis:

Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type.The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

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