Quadratic growth of geodesics on the two-sphere
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911491261726720 |
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| author | Albach, Bernhard |
| author_facet | Albach, Bernhard |
| contents | We prove that for any reversible Finsler metric on S2, the number of prime closed geodesics grows quadratically with respect to length. The main tools are an improvement on Franks' theorem about the number of periodic points of area-preserving annulus maps, and the theory of cylindrical contact homology in the complement of a link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic growth of geodesics on the two-sphere Albach, Bernhard Symplectic Geometry 37Jxx, 53D25, 53D42 We prove that for any reversible Finsler metric on S2, the number of prime closed geodesics grows quadratically with respect to length. The main tools are an improvement on Franks' theorem about the number of periodic points of area-preserving annulus maps, and the theory of cylindrical contact homology in the complement of a link. |
| title | Quadratic growth of geodesics on the two-sphere |
| topic | Symplectic Geometry 37Jxx, 53D25, 53D42 |
| url | https://arxiv.org/abs/2508.00147 |