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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Main Authors: Auslander, Joseph, Johnson, Aimee, Silva, Cesar E, Oxtoby, John C
Format: eBook
Language:English
Published: Providence, Rhode Island American Mathematical Society 29.11.2016
Edition:1
Series:Contemporary Mathematics
Subjects:
Congresses
Measure theory
ISBN:1470422999, 9781470422998
ISSN:0271-4132, 1098-3627
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Abstract 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 Session on Ergodic Theory and Symbolic Dynamics, held from January 17-18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.
AbstractList 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 Session on Ergodic Theory and Symbolic Dynamics, held from January 17-18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.
Author Johnson, Aimee
Oxtoby, John C
Auslander, Joseph
Silva, Cesar E
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Johnson, Aimee
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TableOfContents 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
Title Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby
URI https://www.ams.org/conm/678/
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