Classification of horocycle orbit closures in $ \mathbb{Z} $-covers
Dynamical Systems
2024-09-17 v1 Geometric Topology
Abstract
We fully describe all horocycle orbit closures in -covers of compact hyperbolic surfaces. Our results rely on a careful analysis of the efficiency of all distance minimizing geodesic rays in the cover. As a corollary we obtain in this setting that all non-maximal horocycle orbit closures, while fractal, have integer Hausdorff dimension.
Keywords
Cite
@article{arxiv.2409.10004,
title = {Classification of horocycle orbit closures in $ \mathbb{Z} $-covers},
author = {James Farre and Or Landesberg and Yair Minsky},
journal= {arXiv preprint arXiv:2409.10004},
year = {2024}
}
Comments
55 pages, 8 figures