Tremors and horocycle dynamics on the moduli space 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 in strata of translation surfaces. In the genus two stratum with two singular points, we find orbits which are generic for a measure whose support is strictly contained in the orbit and find orbits which are not generic for any measure. We also describe a horocycle orbit-closure whose Hausdorff dimension is not an integer.
Keywords
Cite
@article{arxiv.2004.04027,
title = {Tremors and horocycle dynamics on the moduli space of translation surfaces},
author = {Jon Chaika and John Smillie and Barak Weiss},
journal= {arXiv preprint arXiv:2004.04027},
year = {2025}
}
Comments
Final version, extensive changes taking into account two detailed referee report. The main results are unchanged, but significant improvements to the argumentation in many places, and several figures added. Thanks to the anonymous referees for the time invested and their many helpful comments