Closed geodesics with prescribed intersection numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909140315537408 |
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| author | Chaubet, Yann |
| author_facet | Chaubet, Yann |
| contents | Let $(Σ, g)$ be a closed, oriented, negatively curved surface, and fix pairwise disjoint simple closed geodesics $γ_{\star,1}, \dots γ_{\star, r}$. We give an asymptotic growth as $L \to +\infty$ of the number of primitive closed geodesic of length less than $L$ intersecting $γ_{\star,j}$ exactly $n_j$ times, where $n_1, \dots, n_r$ are fixed nonnegative integers. This is done by introducing a dynamical scattering operator associated to the surface with boundary obtained by cutting $Σ$ along $γ_{\star,1}, \dots, γ_{\star, r}$ and by using the theory of Pollicott-Ruelle resonances for open systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16301 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Closed geodesics with prescribed intersection numbers Chaubet, Yann Dynamical Systems Differential Geometry 53C22, 37C30, 37D40 Let $(Σ, g)$ be a closed, oriented, negatively curved surface, and fix pairwise disjoint simple closed geodesics $γ_{\star,1}, \dots γ_{\star, r}$. We give an asymptotic growth as $L \to +\infty$ of the number of primitive closed geodesic of length less than $L$ intersecting $γ_{\star,j}$ exactly $n_j$ times, where $n_1, \dots, n_r$ are fixed nonnegative integers. This is done by introducing a dynamical scattering operator associated to the surface with boundary obtained by cutting $Σ$ along $γ_{\star,1}, \dots, γ_{\star, r}$ and by using the theory of Pollicott-Ruelle resonances for open systems. |
| title | Closed geodesics with prescribed intersection numbers |
| topic | Dynamical Systems Differential Geometry 53C22, 37C30, 37D40 |
| url | https://arxiv.org/abs/2103.16301 |