Ergodic theory and dynamical systems : proceedings of the Ergodic Theory Workshops at University of North Carolina at Chapel Hill, 2011-2012 / edited by Idris Assani.

Includes bibliographical references.

Online resource; title from PDF title page (ebrary, viewed March 11, 2014).

Preface; Furstenberg Fractals; 1 Introduction; 2 Furstenberg Fractals; 3 The Fractal Constructions; 4 Density of Non-Recurrent Points; 5 Isometries and Furstenberg Fractals; Idris Assani and Kimberly Presser A Survey of the Return Times Theorem; 1 Origins; 1.1 Averages along Subsequences; 1.2 Weighted Averages; 1.3 Wiener-Wintner Results; 2 Development; 2.1 The BFKO Proof of Bourgain's Return Times Theorem; 2.2 Extensions of the Return Times Theorem; 2.3 Unique Ergodicity and the Return Times Theorem; 2.4 A Joinings Proof of the Return Times Theorem; 3 The MultitermReturn Times Theorem.

3.1 Definitions4 Characteristic Factors; 4.1 Characteristic Factors and the Return Times Theorem; 5 Breaking the Duality; 5.1 Hilbert Transforms; 5.2 The (??1,??1) Case; 6 Other Notes on the Return Times Theorem; 6.1 The Sigma-Finite Case; 6.2 Recent Extensions; 6.3 Wiener-WintnerDynamical Functions; 7 Conclusion; Characterizations of Distal and Equicontinuous Extensions; Averages Along the Squares on the Torus; 1 Introduction and Statement of the Main Results; 2 Preliminary Results and Notation; 3 Proofs of the Main Results; Stepped Hyperplane and Extension of the Three Distance Theorem.

1 Introduction2 Kwapisz's Result for Translation; 3 Continued Fraction Expansions; 3.1 Brun's Algorithm; 3.2 Strong Convergence; 4 Proof of Theorem1.1; 5 Appendix: Proof of Theorem2.4 and Stepped Hyperplane; Remarks on Step Cocycles over Rotations, Centralizers and Coboundaries; 1 Introduction; 2 Preliminaries on Cocycles; 2.1 Cocycles and Group Extension of Dynamical Systems; 2.2 Essential Values, Nonregular Cocycle; 2.3 Z2-Actions and Centralizer; 2.4 Case of an Irrational Rotation; 3 Coboundary Equations for Irrational Rotations; 3.1 Classical Results, Expansion in Basis qna.

3.2 Linear and Multiplicative Equations4 Applications; 4.1 Non-Ergodic Cocycles with Ergodic Compact Quotients; 4.2 Examples of Nontrivial and Trivial Centralizer; 4.3 Example of a Nontrivial Conjugacy in a Group Family; 5 Appendix: Proof of Theorem3.3; Hamilton's Theorem for Smooth Lie Group Actions; 1 Introduction; 2 Preliminaries; 2.1 Fréchet Spaces and Tame Operators; 2.2 Hamilton's Nash-Moser Theoremfor Exact Sequences; 2.3 Cohomology; 3 An Application of Hamilton's Nash-Moser Theoremfor Exact Sequences to Lie Group Actions; 3.1 The Set-Up; 3.2 Tamely Split First Cohomology.

3.3 Existence of Tame Splitting for the Complex3.4 A Perturbation Result; 3.5 A Variation of Theorem 3.6; 4 Possible Applications; Mixing Automorphisms which are Markov Quasi-Equivalent but not Weakly Isomorphic; 1 Introduction; 2 Gaussian Automorphisms and Gaussian Cocycles; 3 Coalescence of Two-Sided Cocycle Extensions; 4 Main Result; On the Strong Convolution Singularity Property; 1 Introduction; 2 Definitions; 2.1 Spectral Theory; 2.2 Joinings; 2.3 Special Flows; 2.4 Continued Fractions; 3 Tools; 4 Smooth Flows on Surfaces; 5 Results; 5.1 New Tools -- The Main Proposition.

5.2 New Tools -- Technical Details.

This is the proceedings of theworkshop on recent developments in ergodic theory and dynamical systemson March 2011and March 2012 at the University of North Carolina at Chapel Hill. Thearticles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These co.

In English.

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