Classification of horocycle orbit closures in $ \mathbb{Z} $-covers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916395985403904 |
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| author | Farre, James Landesberg, Or Minsky, Yair |
| author_facet | Farre, James Landesberg, Or Minsky, Yair |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of horocycle orbit closures in $ \mathbb{Z} $-covers Farre, James Landesberg, Or Minsky, Yair Dynamical Systems Geometric Topology 37D40, 57K20 (Primary) 37A17, 30F60, 22F30, 57K32, 37B20, 37B99 (Secondary) 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. |
| title | Classification of horocycle orbit closures in $ \mathbb{Z} $-covers |
| topic | Dynamical Systems Geometric Topology 37D40, 57K20 (Primary) 37A17, 30F60, 22F30, 57K32, 37B20, 37B99 (Secondary) |
| url | https://arxiv.org/abs/2409.10004 |