Tremors and horocycle dynamics on the oduli spce of translation surfaces

Abstract


We introduce a `tremor’ deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horocycle flow orbits $Uq$ in strata of translation surfaces. In the
genus $2$ stratum $\mathcal{H}(1,1)$ we find orbits $Uq$ which are generic for a measure whose support is strictly contained in $\overline{Uq}$ and find orbits which are not generic for any measure. We also describe a horocycle orbit-closure whose Hausdorff dimension is not an integer.

Authors

Jon Chaika

University of Utah, Salt Lake City, Utah, USA

John Smillie

University of Warwick, Warwick, United Kingdom

Barak Weiss

Tel Aviv University, Tel Aviv, Israel