Topology of horocycles on geometrically finite nonpositively curved surfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914862217560064 |
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| author | Clotet, Sergi Burniol |
| author_facet | Clotet, Sergi Burniol |
| contents | We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topology of horocycles on geometrically finite nonpositively curved surfaces Clotet, Sergi Burniol Dynamical Systems We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow. |
| title | Topology of horocycles on geometrically finite nonpositively curved surfaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2312.07719 |