Eli Glasner's Books

Ergodic Theory via Joinings

By: Eli Glasner

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This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.

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Page Count

402

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470419513

ISBN 13

9781470419516

WAP Systems and Labeled Subshifts

By: Ethan Akin,Eli Glasner

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WAP Systems and Labeled Subshifts

By: Ethan Akin,Eli Glasner

The main object of this work is to present a powerful method of construction of subshifts which the authors use chiefly to construct WAP systems with various properties. Among many other applications of these so-called labeled subshifts, the authors obtain examples of null as well as non-null WAP subshifts, WAP subshifts of arbitrary countable (Birkhoff) height, and completely scrambled WAP systems of arbitrary countable height. They also construct LE but not HAE subshifts and recurrent non-tame subshifts.

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Page Count

128

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437619

ISBN 13

9781470437619

The Topological Dynamics of Ellis Actions

By: Ethan Akin,Joseph Auslander,Eli Glasner

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The Topological Dynamics of Ellis Actions

By: Ethan Akin,Joseph Auslander,Eli Glasner

An Ellis semigroup is a compact space with a semigroup multiplication which is continuous in only one variable. An Ellis action is an action of an Ellis semigroup on a compact space such that for each point in the space the evaluation map from the semigroup to the space is continuous. At first the weak linkage between the topology and the algebra discourages expectations that such structures will have much utility. However, Ellis has demonstrated that these actions arise naturallyfrom classical topological actions of locally compact groups on compact spaces and provide a useful tool for the study of such actions. In fact, via the apparatus of the enveloping semigroup the classical theory of topological dynamics is subsumed by the theory of Ellis actions. The authors'exposition describes and extends Ellis' theory and demonstrates its usefulness by unifying many recently introduced concepts related to proximality and distality. Moreover, this approach leads to several results which are new even in the classical setup.

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Page Count

166

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821841882

ISBN 13

9780821841884

Ergodic Theory via Joinings

By: Eli Glasner

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Ergodic Theory via Joinings

By: Eli Glasner

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N/A

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Solve jigsaw puzzle

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Page Count

402

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470419513

ISBN 13

9781470419516

The Topological Dynamics of Ellis Actions

By: Ethan Akin,Joseph Auslander,Eli Glasner

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The Topological Dynamics of Ellis Actions

By: Ethan Akin,Joseph Auslander,Eli Glasner

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Page Count

166

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821841882

ISBN 13

9780821841884

WAP Systems and Labeled Subshifts

By: Ethan Akin,Eli Glasner

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WAP Systems and Labeled Subshifts

By: Ethan Akin,Eli Glasner

The main object of this work is to present a powerful method of construction of subshifts which we use chiefly to construct WAP systems with various properties. Among many other applications of this so called labeled subshifts, we obtain examples of null as well as non-null WAP subshifts, WAP subshifts of arbitrary countable (Birkhoff) height, and completely scrambled WAP systems of arbitrary countable height. We also construct LE but not HAE subshifts, and recurrent non-tame subshifts.

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Page Count

116

Published Date

ISBN 10

147045503X

ISBN 13

9781470455033

Book's by Eli Glasner

Ergodic Theory via Joinings

Ergodic Theory via Joinings

WAP Systems and Labeled Subshifts

WAP Systems and Labeled Subshifts

The Topological Dynamics of Ellis Actions

The Topological Dynamics of Ellis Actions

Ergodic Theory via Joinings

Ergodic Theory via Joinings

The Topological Dynamics of Ellis Actions

The Topological Dynamics of Ellis Actions

WAP Systems and Labeled Subshifts

WAP Systems and Labeled Subshifts

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