Ergodic Theory and Zd Actions

by Edited by Mark Pollicott , Klaus Schmidt

• ISBN13: 9780521576888
• ISBN10: 0521576881
• Format: Paperback
• Copyright: 1996-04-26
• Publisher: Cambridge University Press

Summary

The classical theory of dynamical systems has tended to concentrate on Z-actions or R-actions. However in recent years there has been considerable progress in the study of higher dimensional actions (i.e. Zd or Rd with d>1). This book represents the proceedings of the 1993-4 Warwick Symposium on Zd actions. It comprises a mixture of surveys and original articles that span many of the diverse facets of the subject, including important connections with statistical mechanics, number theory and algebra. Researchers in ergodic theory and related fields will find that this book is an invaluable resource.

Table of Contents

Part I. Surveys: 1. Ergodic Ramsey theory V. Bergelson

2. Flows on homogeneous spaces S. Dani

3. The variational principle for Hausdorff dimension D. Gatzouras and Y. Peres

4. Boundaries of invariant Markov operators V. Kaimanovic

5. Squaring and cubing the circle W. Parry

6. Recent K-theoretic invariants for dynamical systems I. Putnam

7. Miles of tiles C. Radin

8. Overlapping cylinders K. Simon

Part II. Research Papers: 1. Uniformity in the polynomial Szemerdi theorem V. Bergelson and R. McCutcheon

2. Some 2-d symbolic dynamic systems R. Burton and J. Steif

3. Rigid subshifts K. Eloranta

4. Entropy of graphs, semigroups and groups S. Friedland

5. Integers in linear numeration systems C. Frougny and B. Solomyak

6. Ergodic transforms conjugate to their inverses G. Goodson

7. Approximation by periodic transformations A. Iwanik

8. Invariant s-algebras and their applications B. Kaminski

9. Large deviations for paths and configurations counting Y. Kifer

10. A zeta function for Zd actions D. Lind

11. The dynamical theory of tilings and quasicrystals E. Robinson

12. Approximations of groups and group actions, Cayley topology A. Stepin.