Dynamical systems and group actions / / Lewis Bowen, Rostislav Grigorchuk, Yaroslav Vorobets, editors

• Record Nr.: UNINA9910788637403321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2012]; ©2012
• ISBN: 0-8218-8539-1
• Descrizione fisica: 1 online resource (280 p.)
• Collana: Contemporary mathematics, ; 567 , 0271-4132
• Classificazione: 37Axx37Bxx37Dxx20Exx20Pxx20Nxx22Fxx
• Disciplina: 515/.39
• Soggetti: Ergodic theory; Topological dynamics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Preface -- Bibliography -- Hyperfinite actions on countable sets and probability measure spaces -- 1. Introduction -- Acknowledgement -- 2. The Stone-Cech compactification -- 3. Geometrically hyperfinite actions -- 4. Graphs and graphings -- 5. On faithfulness -- 6. On a problem of van Douwen -- 7. A topologically free, hyperfinite action of a nonamenable group -- References -- A road to the spectral radius of transfer operators -- 1. Introduction -- 2. Reversible dynamics. Spectral radius and ergodic measures -- 3. Irreversible-reversible dynamics -- 4. Irreversible dynamics. Weighted shifts and Perron-Frobenius operators. Spectral radius and entropy -- 5. Spectral potential of a transfer operator. Convexity, Legendre duality and thermodynamics -- 6. Spectral potentials and dual entropy -- 7. Entropy and variational principle for transfer operators -- 8. Properties of -entropy. Entropy Statistic Theorem and Variational Principle for -entropy -- 9. Variational principle for weighted shift operators -- 10. Multiterm functional operators. Variational principles etc. -- References -- A condition for weak mixing of induced IETs -- 1. IETs: Minimality, ergodicity and mixing -- 2. The results -- 3. Some notation, terminology and lemmas -- 4. Proof of Theorem 3 -- 5. Proof of Theorem 2 -- 6. Proof of Proposition 3 -- 7. Two extensions of Theorem 1 -- 8. Final comments -- References -- Every countably infinite group is almost Ornstein -- 1. Introduction -- 2. Preliminaries ; -- 3. Almost Ornstein groups -- 4. Measurable subgroups -- 5. Ornstein groups -- References -- Fair dice-like hyperbolic systems -- 1. Introduction -- 2. Definitions and main results -- Concluding remarks -- References -- Complexity and heights of tori -- 1. Introduction -- 2. Spectral preliminaries for discrete tori -- 3. Spectral preliminaries for continuous tori -- 4. Asymptotics -- 5. Proof of the corollaries -- References -- Flows with uncountable but meager group of self-similarities -- 0. Introduction -- 1. Gaussian examples -- 2. Poisson flows -- 3. Concluding remarks and problems -- References -- The universal minimal space of the homeomorphism group of a h-homogeneous space -- 1. Introduction -- 2. Preliminaries -- 3. Basic properties of h-homogeneous spaces -- 4. Calculation of the universal minimal space -- References -- Generic eigenvalues, generic factors and weak dis-jointness -- 1. Introduction -- 2. Generic eigenvalues and weakly scattering -- 3. Generic homomorphisms, generic factors and weak disjointness -- 4. Relations among several scattering properties -- 5. Scattering properties in an almost equicontinuous system -- References -- Around King's rank-one theorems: Flows and actions -- 1. Introduction -- 2. Preliminaries and notations -- 3. Rank-one flows.