Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation

Uniquely Ergodic Minimal Tiling Spaces with Positive Entropy

Strictly ergodic spaces of tilings with positive entropy are constructed using tools from information and probability theory. Statistical estimates are made to create a one-dimensional subshift with these dynamical properties, yielding a space of repetitive tilings of R with finite local complexity that is also equivalent to a symbolic dynamical system with a Z action.

Limit Sets of Weil-petersson Geodesics

In this paper we investigate limit sets of Weil-Petersson geodesics in the Thurston compactification of Teichmüller space.

Existence of Non-uniform Cocycles on Uniquely Ergodic Systems

Nondivergence of Horocyclic Flows on Moduli Space

The earthquake flow and the Teichmüller horocycle flow are flows on bundles over the Riemann moduli space of a surface, and are similar in many respects to unipotent flows on homogeneous spaces of Lie groups. In analogy with results of Margulis, Dani and others in the homogeneous space setting, we prove strong nondivergence results for these flows. This extends previous work of Veech. As coroll...

A Uniquely Ergodic Cellular Automaton

We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on the self-simulating automaton of Gács. We also prove related results of dynamical and computational nature, including the undecidability of unique ergodicity,...