arXiv:2409.10004 Abstract | arXiv Analytics

arXiv:2409.10004 [math.DS]Abstract References Reviews Resources

Classification of horocycle orbit closures in $ \mathbb{Z} $-covers

Published 2024-09-16Version 1

We fully describe all horocycle orbit closures in $ \mathbb{Z} $-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.

Comments: 55 pages, 8 figures

Categories: math.DS, math.GT

Subjects: 37D40, 57K20, 37A17, 30F60, 22F30, 57K32, 37B20, 37B99

Keywords: classification, non-maximal horocycle orbit closures, compact hyperbolic surfaces, integer hausdorff dimension, distance minimizing geodesic rays

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