Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915571687227392 |
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| author | Sy, Amadou |
| author_facet | Sy, Amadou |
| contents | The aim of this article is to show that if there exists $u \in Ω_{h} \subset T^{1}S$ an infinite quasi-minimizing ray which do not intersect any closed geodesic on the surface $S$ (untwisted flute), then $T_{u}=\{ t \in \mathbb{R} \; ; \; g_{t}u \in \overline{h_{\mathbb{R}}u} \}=\{0\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute Sy, Amadou Geometric Topology The aim of this article is to show that if there exists $u \in Ω_{h} \subset T^{1}S$ an infinite quasi-minimizing ray which do not intersect any closed geodesic on the surface $S$ (untwisted flute), then $T_{u}=\{ t \in \mathbb{R} \; ; \; g_{t}u \in \overline{h_{\mathbb{R}}u} \}=\{0\}$. |
| title | Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2510.20464 |