Year: 2026
Type: article
Abstract: We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horocycle flow orbits $U_q$ in strata of translation surfaces. In the genus $2$ stratum $\mathcal{H}(1,1)$ we find orbits $U_q$ which are generic for a measure whose support is strictly contained in $\overline{U_q}$ and find orbits which are not generic for any measure. We also describe a horocycle orbit-closure whose Hausdorff dimension is not an integer.
Source: Annals of Mathematics
Authors: Jon Chaika, John Smillie, Barak Weiss
Institutions: Rice University, University of Warwick, Tel Aviv University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167058708