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Invitation to Ergodic Theory

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 202/5 ( reviews)

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Book Synopsis Invitation to Ergodic Theory by : César Ernesto Silva

Download or read book Invitation to Ergodic Theory written by César Ernesto Silva. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: "Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian-Kakutani transformation, the Gauss transformation, and the Chacon transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem."--BOOK JACKET.

Ergodic Theory

2023-07-31 Mathematics
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Release : 2023-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva. This book was released on 2023-07-31. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

An Introduction to Infinite Ergodic Theory

1997 Mathematics
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Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 944/5 ( reviews)

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Book Synopsis An Introduction to Infinite Ergodic Theory by : Jon Aaronson

Download or read book An Introduction to Infinite Ergodic Theory written by Jon Aaronson. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.

Ergodic Theory Via Joinings

2014-05-21 MATHEMATICS
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Release : 2014-05-21
Genre : MATHEMATICS
Kind : eBook
Book Rating : 286/5 ( reviews)

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Book Synopsis Ergodic Theory Via Joinings by : Eli Glasner

Download or read book Ergodic Theory Via Joinings written by Eli Glasner. This book was released on 2014-05-21. Available in PDF, EPUB and Kindle. Book excerpt: This text 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 text presents the entire theory from a joining perspective. Another 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.

Lectures on Ergodic Theory

2017-12-13 Mathematics
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Release : 2017-12-13
Genre : Mathematics
Kind : eBook
Book Rating : 890/5 ( reviews)

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Book Synopsis Lectures on Ergodic Theory by : Paul R. Halmos

Download or read book Lectures on Ergodic Theory written by Paul R. Halmos. This book was released on 2017-12-13. Available in PDF, EPUB and Kindle. Book excerpt: This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

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