Récurrence ou non minimalité des adhérences des d'orbites irréguliéres du flot horocyclique de finesse infinie
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910109886578688 |
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| author | Sy, Amadou Gaye, Masseye |
| author_facet | Sy, Amadou Gaye, Masseye |
| contents | The topological dynamics of the horocyclic flow $h_{\mathbb{R}}$ on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular, on such a surface, the flow $h_{\mathbb{R}}$ is minimal, or the minimal sets are the periodic orbits. When the surface is geometrically infinite, the situation is more complex, and the presence of possible non-closed and non-dense orbits, called irregular orbits, complicates the description of minimal sets. In this text, we will show that such an orbit is recurrent, or its closure is non-$h_{\mathbb{R}}$ minimal. This would allow us to almost complete the description of $h_{\mathbb{R}}$-minimal sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Récurrence ou non minimalité des adhérences des d'orbites irréguliéres du flot horocyclique de finesse infinie Sy, Amadou Gaye, Masseye Geometric Topology The topological dynamics of the horocyclic flow $h_{\mathbb{R}}$ on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular, on such a surface, the flow $h_{\mathbb{R}}$ is minimal, or the minimal sets are the periodic orbits. When the surface is geometrically infinite, the situation is more complex, and the presence of possible non-closed and non-dense orbits, called irregular orbits, complicates the description of minimal sets. In this text, we will show that such an orbit is recurrent, or its closure is non-$h_{\mathbb{R}}$ minimal. This would allow us to almost complete the description of $h_{\mathbb{R}}$-minimal sets. |
| title | Récurrence ou non minimalité des adhérences des d'orbites irréguliéres du flot horocyclique de finesse infinie |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2512.13519 |