Proof of the $C^2$-stability conjecture for geodesic flows of closed surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929344341868544 |
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| author | Contreras, Gonzalo Mazzucchelli, Marco |
| author_facet | Contreras, Gonzalo Mazzucchelli, Marco |
| contents | We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed surfaces: a $C^2$-structurally stable Riemannian geodesic flow of a closed surface is Anosov. In order to prove these statements, we establish a general result that may be of independent interest and provides sufficient conditions for a Reeb flow of a closed 3-manifold to be Anosov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10704 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Proof of the $C^2$-stability conjecture for geodesic flows of closed surfaces Contreras, Gonzalo Mazzucchelli, Marco Dynamical Systems Differential Geometry Symplectic Geometry 37D40, 53D10, 53C22 We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed surfaces: a $C^2$-structurally stable Riemannian geodesic flow of a closed surface is Anosov. In order to prove these statements, we establish a general result that may be of independent interest and provides sufficient conditions for a Reeb flow of a closed 3-manifold to be Anosov. |
| title | Proof of the $C^2$-stability conjecture for geodesic flows of closed surfaces |
| topic | Dynamical Systems Differential Geometry Symplectic Geometry 37D40, 53D10, 53C22 |
| url | https://arxiv.org/abs/2109.10704 |