An Introduction to Ergodic Theory by Peter Walters

An Introduction to Ergodic Theory by Peter Walters

This text provides an introduction to ergodic theory suitable for readers knowing basic measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped the reader will be ready to tackle research papers after reading the book. The first part of the text is concerned with measure-preserving transformations of probability spaces; recurrence properties, mixing properties, the Birkhoff ergodic theorem, isomorphism and spectral isomorphism, and entropy theory are discussed. Some examples are described and are studied in detail when new properties are presented. The second part of the text focuses on the ergodic theory of continuous transformations of compact metrizable spaces. The family of invariant probability measures for such a transformation is studied and related to properties of the transformation such as topological traitivity, minimality, the size of the non-wandering set, and existence of periodic points. Topological entropy is introduced and related to measure-theoretic entropy. Topological pressure and equilibrium states are discussed, and a proof is given of the variational principle that relates pressure to measure-theoretic entropies. Several examples are studied in detail. The final chapter outlines significant results and some applications of ergodic theory to other branches of mathematics.

Many people refer to Peter Walters as 'Mr Coventry,' a label he has gained as a result of his several award-winning newspaper pieces about the city. He's presently working as a freelance copywriter. During the 1970s, Peter has lived in Coventry. He is a founding member of the City of Coventry Ambassadors Group and an active member of a local historical campaigning organisation (the Coventry Society).

SKU	Unavailable
ISBN 13	9780387951522
ISBN 10	0387951520
Title	An Introduction to Ergodic Theory
Author	Peter Walters
Series	Graduate Texts In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer-Verlag New York Inc.
Year published	2000-10-06
Number of pages	250
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.