Classification of horocycle orbit closures in $ \mathbb{Z} $-covers
| Autor: | Farre, James, Landesberg, Or, Minsky, Yair |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 55 pages, 8 figures |
| Databáze: | arXiv |
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