Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby
This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30-31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27-29, 2012, at Williams College; and the AMS Special Sessi...
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| Hlavní autoři: | , , , |
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Providence, Rhode Island
American Mathematical Society
29.11.2016
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| Vydání: | 1 |
| Edice: | Contemporary Mathematics |
| Témata: | |
| ISBN: | 1470422999, 9781470422998 |
| ISSN: | 0271-4132, 1098-3627 |
| On-line přístup: | Získat plný text |
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- Conjugacy in the Cantor set automorphism group -- The mathematical work of John C. Oxtoby -- The C̆ech cohomology and the spectrum for 1-dimensional tiling systems -- Markov diagrams for some non-Markovian systems -- Contractive spaces and relatively contractive maps -- Mandelpinski structures in the parameter planes of rational maps -- Substitutions and Möbius disjointness -- Subshifts with slowly growing numbers of follower sets -- Haar measures and Hausdorff dimensions of <inline-formula content-type="math/mathml"> p p </inline-formula>-adic Julia sets -- Lebesgue measure theoretic dynamics of rational maps -- The inverse problem for canonically bounded rank-one transformations -- Higher dimensional shift spaces with shear -- Hereditary subshifts whose simplex of invariant measures is Poulsen -- Substitutions, symbolic codings, and discrepancy -- Nearly continuous even Kakutani equivalence of nearly continuously rank-one transformations -- Dynamics of self-similar interval exchange transformations on three intervals
- Cover -- Title page -- Contents -- Preface -- Conjugacy in the Cantor set automorphism group -- Introduction -- 1. Relations and Maps -- 2. Representations of Mappings via Indexed Partitions -- 3. Representation Characterizations -- 4. Examples -- References -- The mathematical work of John C. Oxtoby -- 1. Introduction -- 2. Biographical Note -- 3. Category -- 4. Homeomorphic Measures -- 5. Ergodic Sets -- 6. Banach-Mazur Game -- 7. Other work and Measure and Category -- Acknowledgement -- References -- The Cech cohomology and the spectrum for 1-dimensional tiling systems -- 1. Introduction -- 2. Discrete Dynamical Systems -- 3. Flows and tiling systems -- 4. Substitution tilings -- 5. Examples -- 6. Appendix: Remarks on Bruschlinsky's theorem -- References -- Markov diagrams for some non-Markovian systems -- 1. Introduction -- 2. Background -- 3. Hofbauer-Buzzi Markov diagrams -- 4. Markov diagrams for one-sided Sturmian systems -- 5. General properties of HB diagrams -- 6. The Morse minimal subshift -- 7. Conclusion and Further Directions -- Acknowledgement -- References -- Contractive spaces and relatively contractive maps -- 1. Introduction -- 2. Group Actions on Probability Spaces -- 3. Contractive Spaces -- 4. Relatively Contractive Maps -- 5. The Factor Theorems -- 6. Rigidity of Actions of Lattices -- Acknowledgments -- References -- Mandelpinski structures in the parameter planes of rational maps -- 1. Preliminaries -- 2. Mandelpinski Necklaces -- 3. Dynamics on Sierpinski Curve Julia Sets -- 4. Mandelpinski Spokes -- 5. The Mandelpinski Maze -- 6. Open Questions -- References -- Substitutions and Möbius disjointness -- 1. Introduction -- 2. Basic tools -- 3. Basic objects -- 4. Sarnak's conjecture for finite group extensions -- 5. Applications -- 6. Spectral approach and other methods -- References
- Subshifts with slowly growing numbers of follower sets -- 1. Introduction -- 2. Definitions and preliminaries -- 3. An example with many more predecessor sets than follower sets -- 4. Main Results -- References -- Haar measures and Hausdorff dimensions of -adic Julia sets -- 1. Introduction and statement of main result -- 2. Haar measure and Hausdorff dimension in finite extensions -- 3. Haar measure and Hausdorff dimension of Julia sets -- 4. Examples and discussion -- References -- Lebesgue measure theoretic dynamics of rational maps -- 1. Introduction -- 2. Preliminary definitions and the first examples -- 3. A family of ergodic and exact nonpolynomial maps with an invariant probability measure equivalent to ℓ -- 4. Two dimensional Lebesgue measure -- References -- The inverse problem for canonically bounded rank-one transformations -- 1. Introduction -- 2. Arguments -- References -- Higher dimensional shift spaces with shear -- 1. Background Definitions -- 2. Shift Spaces with Shear: Definitions and Examples -- 3. Generalized Shift Products -- 4. \mb ^{ -1}-Shear in \mb ^{ } Shift Spaces -- 5. \mb ^{ -1}-Shear in \mb ^{ } Shifts of Finite Type -- 6. \mb ^{ -1}-Shear in \mb ^{ } Sofic Shifts -- 7. Future Research Questions -- References -- Hereditary subshifts whose simplex of invariant measures is Poulsen -- 1. Introduction -- 2. Proof of Theorem 1.2 for of zero entropy -- 3. Sketch of the proof of Theorem 1.2 for general -- 4. Hereditary system of positive entropy whose simplex of invariant measures is not Poulsen -- References -- Substitutions, symbolic codings, and discrepancy -- 1. Introduction -- 2. Terminology -- 3. History -- 4. Self-Similar Systems -- 5. Dynamically Defined Substitution Schemes -- 6. Systems Coded by Dynamically Defined Substitutions -- 7. Conclusion -- Acknowledgments -- References
- Nearly continuous even Kakutani equivalence of nearly continuously rank-one transformations -- 1. Introduction -- 2. Definitions and Basic Facts -- 3. Theorem 1.1 -- 4. Nearly Unique Ergodicity and Non-even n.c. Kakutani Equivalence -- 5. Nearly Continuously Rank-One -- 6. Conclusion -- References -- Dynamics of self-similar interval exchange transformations on three intervals -- 1. Introduction -- 2. Preliminaries -- 3. 3-IETs are not Rigid -- 4. Minimal Self-Joinings of 3-IETs -- Acknowledgements -- References -- Back Cover