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Classification of horocycle orbit closures in $ \mathbb{Z} $-covers (2409.10004v1)
Published 16 Sep 2024 in math.DS and math.GT
Abstract: 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.
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