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This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill.
The articles 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 contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.
Idris Assani, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
- Daniela Damjanovic - "Hamilton’ s theorem for smooth Lie group actions"
- Ethan Akin - "Furstenberg Fractals"
- Omri Sarig and Martin Schmoll - "Adic flows, Transversal flows, Horocycle flows"
- Zoltan Buczolich - "Averages along the squares on the torus"
- Nicolas Chevallier - "Stepped hyperplane and extension of the three distance theorem"
- Joseph Auslander - " Characterizations of distal and equicontinuous extensions"
- Idris Assani and Kim Presser- "A survey on the return times theorem"
- Joanna Kaluga - "On the strong convolution singularity property"
- Carlos Matheus Santos - "On the fractal geometry of non-uniformly hyperbolic horseshoes"
- Kelly Funk - "Topologically Weakly Mixing Homeomorphisms of the Two-Torus that are Uniformly Rigid"