Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913514352803840 |
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| author | Mamani, Edhin F. Ruggiero, Rafael |
| author_facet | Mamani, Edhin F. Ruggiero, Rafael |
| contents | Let $(M,g)$ be a compact connected $C^{\infty}$ surface without conjugate points of genus greater than one. We show that set of geodesics without strips forms a dense set of orbits in the unit tangent bundle. This fact was known assuming no focal points as a consequence of a result of Coudène and Shapira. They showed that flat strips are periodic and hence form a set of zero measure in the unit tangent bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points Mamani, Edhin F. Ruggiero, Rafael Dynamical Systems Let $(M,g)$ be a compact connected $C^{\infty}$ surface without conjugate points of genus greater than one. We show that set of geodesics without strips forms a dense set of orbits in the unit tangent bundle. This fact was known assuming no focal points as a consequence of a result of Coudène and Shapira. They showed that flat strips are periodic and hence form a set of zero measure in the unit tangent bundle. |
| title | Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2409.15768 |