Ergodic theory of Zd actions : proceedings of the Warwick symposium, 1993-4 / edited by Mark Pollicott, Klaus Schmidt.

Title from PDF title page (viewed on Apr. 9, 2013).

On t.p. "d" in "Zd" is superscript.

Includes bibliographical references.

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.

Cover; Title; Copyright; Contents; INTRODUCTION; Ergodic Ramsey Theory-an Update; 0. Introduction.; 1. Three main principles of Ramsey theory and its connectionwith the ergodic theory of multiple recurrence.; 2. Special case of polynomial Szemeredi theorem: single recurrence.; 3. Discourse on /?N and some of its applications.; 4. IP-polynomials, recurrence, and polynomialHales-Jewett theorem.; 5. Some open problems and conjectures.; REFERENCES; Flows on homogeneous spaces: a review; Introduction; 1 Homogeneous spaces -- an overview; 2 Ergodicity; 3 Dense orbits; some early results

4 Conjectures of Oppenheim and Raghunathan 5 Invariant measures of unipotent flows; 6 Homecoming of trajectories of unipotent flows; 7 Distribution and closures of orbits; 8 Aftermath of Ratner's work; 9 Miscellanea; References; The Variational Principle For Hausdorff Dimension:A Survey; 1. Introduction; 2. The conformal case; 3. Nonconformal maps; 4. Concluding remarks; REFERENCES; Boundaries Of Invariant Markov Operators The Identification Problem; 0.1. General Markov operators.; 0.2. Examples of Markov operators.; 0.3. Invariant Markov operators.

0.4. Quotients of Markov operators.0.5. Boundary theory of Markov operators.; 1. THE MARTIN BOUNDARY; 2. THE POISSON BOUNDARY; 3. SEMI-SIMPLE LIE GROUPS AND SYMMETRIC SPACES; REFERENCES; Squaring And Cubing The Circle -Rudolph'S Theorem; 1. Generalities; 2. Endomorphisms of the circle; 3. Rudolph's comparative entropy lemma; References; A Survey of Recent K-Theoretic Invariants for Dynamical Systems; Section 1: Introduction; Section 2: Topological Equivalence Relations; Section 3: Examples; Section 4: C*-algebras; Section 5: K-Theory; Section 6: Invariant Measures

Section 7: K-Theory of AF-Equivalence RelationsSection 8: Singly Generated Equivalence Relations and the Pimsner-Voiculescu Sequence; Section 9: Orbit Equivalence; Section 10: Factors and Sub-Equivalence Relations; References; Miles of Tile*; I. The Wang/Berger phenomenon; II. The pinwheel and Penrose tilings; III. Statistical mechanics and tilings; IV. A new form of symmetry; Bibliography; Overlapping cylinders: the size of a dynamically defined Cantor-set; 1 Introduction; 2 The self similar case in dimension one; 3 Horseshoes with overlapping cylinders; References

Uniformity in the Polynomial Szemerédi Theorem0. Introduction; 1. Measure theoretic preliminaries.; 2. Weakly mixing extensions.; 3. Uniform polynomial Szemeredi theorem for distal systems.; 4. Appendix: Proof of Theorem 3.2.; REFERENCES; Some 2-d Symbolic Dynamical Systems: Entropy and Mixing; 1 Introduction; 2 The Iceberg Model: Measures of Maximal Entropy and Mixing; 3 The Generalized Hard Core Model: Measuresof Maximal Entropy and Mixing; 4 Spanning Trees and Dominoes: Measuresof Maximal Entropy and Mixing; References; A note on certain rigid subshifts; Abstract; Introduction; 1. Spaces

English.

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