Ergodic Theory and Zd Actions

A mixture of surveys and original articles that span the theory of Zd actions.

Mark Pollicott (Edited by), Klaus Schmidt (Edited by)

9780521576888, Cambridge University Press

Paperback, published 28 March 1996

496 pages
22.8 x 15.2 x 2.8 cm, 0.666 kg

'The book will serve as a valuable resource of information and motivation for specialists.' European Mathematical Society Newsletter

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]