Ergodic Theory of Zd Actions (London Mathematical Society Lecture Note Series)

The classical theory of dynamical systems has tended to concentrate on Z-actions or R-actions. In recent years, however, 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. CONTENTS......Page 5 Introduction......Page 7 1. V. Bergelson Ergodic Ramsey Theory......Page 9 2. S.G. Dani, Flows on homogeneous spaces......Page 71 3. D. Gatzouras and Y. Peres, The variational principle for Hausdorff dimension......Page 121 4. V. Kaimanovich, Boundaries of invariant Markov Operators: The identification problem......Page 135 5. W. Parry, Squaring and cubing the circle - Rudolph's theorem......Page 185 6. I. Putnam, A survey of recent K-theoretic invariants for dynamical systems......Page 193 7. C. Radin, Miles of Tiles......Page 245 8. K. Simon, Overlapping cylinders: the size of a dynamically defined Cantor-set......Page 267 1. V. Bergelson and R. McCutcheon, Uniformity in the polynomial Szemerdi theorem......Page 281 2. R. Burton and J. Steif, Some 2-d symbolic dynamical systems: Entropy and mixing......Page 305 3. K. Eloranta, A note on certain rigid subshifts......Page 315 4. S. Friedland, Entropy of graphs, semigroups and groups......Page 327 5. C. Frougny and B. Solomyak, On representation of integers in Linear Numeration Systems......Page 353 6. G. Goodson, The structure of ergodic transformations conjugate to their inverses......Page 377 7. A. Iwanik, Approximatiom by periodic transformations and diophantine approximation of the spectrum......Page 395 8. B. Kaminski, Invariant v-algebras for Zd-actions and their applications......Page 411 9. Y. Kifer, Large deviations for paths and configurations counting......Page 423 10.D. Lind, A zeta function for Zd-actions......Page 441 11.E.A. Robinson, The dynamical theory of tilings and Quasicrystallography......Page 459 12.A. Stepin, Approximations of groups and group actions, Cayley topology......Page 483 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. A mixture of surveys and original articles that span the theory of Zd actions.