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Ergodic theory of Zd actions : proceedings of the Warwick symposium, 1993-4 /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1996.
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| Colección: | London Mathematical Society lecture note series ;
228. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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