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An Introduction to Ergodic Theory

2000-10-06 Mathematics
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Release : 2000-10-06
Genre : Mathematics
Kind : eBook
Book Rating : 522/5 ( reviews)

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Book Synopsis An Introduction to Ergodic Theory by : Peter Walters

Download or read book An Introduction to Ergodic Theory written by Peter Walters. This book was released on 2000-10-06. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.

Ergodic Theory

2010-09-11 Mathematics
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Release : 2010-09-11
Genre : Mathematics
Kind : eBook
Book Rating : 215/5 ( reviews)

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Book Synopsis Ergodic Theory by : Manfred Einsiedler

Download or read book Ergodic Theory written by Manfred Einsiedler. This book was released on 2010-09-11. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Ergodic Theory — Introductory Lectures

2007-12-03 Mathematics
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Release : 2007-12-03
Genre : Mathematics
Kind : eBook
Book Rating : 949/5 ( reviews)

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Book Synopsis Ergodic Theory — Introductory Lectures by : P. Walters

Download or read book Ergodic Theory — Introductory Lectures written by P. Walters. This book was released on 2007-12-03. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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.

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