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Preface
In 1970 I gave a graduate course in ergodic theory at the University of Maryland
in College Park, and these lectures were the basis of the Springer Lecture Notes in
Mathematics Volume 458 called "Ergodic Theory—Introductory Lectures" which
was published in 1975. This volume is now out of print, so I decided to revise and
add to the contents of these notes. I have updated the earlier chapters and have added
some new chapters on the ergodic theory of continuous transformations of compact
metric spaces. In particular, I have included some material on topological pressure
and equilibrium states. In recent years there have been some fascinating interactions
of ergodic theory with differentiable dynamics, differential geometry, number theory,
von Neumann algebras, probability theory, statistical mechanics, and other topics. In
Chapter 10 I have briefly described some of these and given references to some of
the others. I hope that this book will give the reader enough foundation to tackle the
research papers on ergodic theory and its applications.
I would like to dedicate this volume to the memory of Rufus Bowen who died on
July 30, 1978 at the age of 31. He made outstanding contributions to ergodic theory
and his friendship enhanced the lives of all who knew him.
April, 1981
PETER WALTERS
