Dynamical Systems, Ergodic Theory, and Probability : in Memory of Kolya Chernov.

Cover -- Title page -- Contents -- Preface -- N. I. CHERNOV (1956-2014) -- Joint coboundaries -- 1. Introduction -- 2. Role of coboundaries in rate of norm convergence -- 3. Algebra gives common coboundaries -- 4. Coboundaries and automatic continuity -- 5. Generic case for no common coboundaries -- 6. General cases -- 7. Joint under powers -- 8. Various constructions -- 9. Constructions that are not coboundaries -- 10. First Category -- 11. Finite step function coboundaries -- 12. Weak mixing coboundaries -- 13. Unresolved Issues -- Acknowledgments -- References -- Convergence of moments for dispersing billiards with cusps -- 1. Introduction -- 2. Billiards with cusps -- 3. Proof of Theorem 4 -- 4. Young tower and equidistribution for -- 5. Proof of Lemma 3.1 -- 6. Proof of Lemma 3.3 -- Appendix A. A probabilistic model -- Appendix B. Proof of Proposition 1.4 -- References -- Weak pseudo-physical measures and Pesin's entropy formula for Anosov ¹-diffeomorphisms. -- 1. Introduction -- 2. Properties of the weak pseudo-physical measures -- 3. Sufficient condition for Pesin's Entropy Formula -- 4. Necessary condition for Pesin's Entropy Formula -- References -- No-slip billiards in dimension two -- 1. Introduction -- 2. Periodic and bounded orbits -- 3. Other examples of no-slip billiards -- References -- How sticky is the chaos/order boundary? -- 1. Introduction -- 2. Previous results -- 3. Development of the theory -- 4. Proofs of the theorems -- 5. Lemmas and their proofs -- Acknowledgements -- References -- Bouncing in gravitational field -- 1. Introduction -- 2. Statement of the result -- 3. Three Lemmas -- 4. Proof of the Theorem -- 5. Local versus global minimizers -- References -- A derivation of the Poisson law for returns of smooth maps with certain geometrical properties -- 1. Introduction -- 2. Assumptions and main results.

3. Proof of Theorem 1 -- 4. Very short returns -- 5. Poisson approximation theorem -- 6. Proof of Theorem 2 -- 7. Example -- References -- Rigidity for a class of generalized interval exchange transformations -- 1. Introduction and statement of the results -- 2. Proof of the main theorem -- References -- Homotopical complexity of a 3 billiard flow -- 1. Introduction -- 2. Prerequisites. Model and Geometry of Orbits -- 3. The admissible rotation set -- 4. Comparing our results with geodesic flows -- 5. Topological entropy of the flow -- Acknowledgment -- References -- Mixing properties of some maps with countable Markov partitions -- 1. Statement of results -- 2. Hölder properties of log( ^{ } ( )) in the phase space. -- 3. Proof of the main theorem -- 4. One model with strong contraction -- Acknowledgments -- References -- Eigenfunctions of Laplacians in some two-dimensional domains -- 1. Introduction -- 2. Discrete Approximations of Laplacians -- Acknowledgments -- References -- Multidimensional hyperbolic billiards -- 1. Introduction -- 2. A summary -- 3. Qualitative properties of multidimensional billiards -- 4. Quantitative properties of multidimensional billiards -- Acknowledgements -- References -- Homoclinic intersections for geodesic flows on convex spheres -- 1. Introduction -- 2. Preliminaries -- 3. Perturbations of closed geodesics -- 4. Homoclinic intersections for hyperbolic closed geodesics -- Acknowledgments -- References -- Decay of correlations for billiards with flat points I: channel effects -- 1. Background and the main results -- 2. General scheme -- 3. Construction of the induced map ( , ) -- 4. Uniform Hyperbolicity of ( , ,\hmu) -- 5. Distribution of the first return time function -- 6. Singularity set of the induced map ( , ) -- 7. Regularity of unstable curves -- 8. Exponential decay rates for the induced system.

9. Proof of the main Theorems. -- 10. Proof of Proposition 10 -- Acknowledgment -- References -- Decay of correlations for billiards with flat points II: cusps effect -- 1. Background and the main results. -- 2. General scheme -- 3. The corner series -- 4. Hyperbolicity of ( , ) -- 5. Distribution of the return time function -- 6. Exponential decay rates for the induced system -- 7. Proof of the main Theorems -- 8. General models with cusps -- 9. Appendix: Proof of Proposition 4. -- Acknowledgement -- References -- Back Cover.

This volume contains the proceedings of the Conference on Dynamical Systems, Ergodic Theory, and Probability, which was dedicated to the memory of Nikolai Chernov, held from May 18-20, 2015, at the University of Alabama at Birmingham, Birmingham, Alabama. The book is devoted to recent advances in the theory of chaotic and weakly chaotic dynamical systems and its applications to statistical mechanics. The papers present new original results as well as comprehensive surveys.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.