Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913423618473984 |
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| author | Jézéquel, Malo |
| author_facet | Jézéquel, Malo |
| contents | We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension $d$, the number of resonances larger than $r$ is a $\mathcal{O}(|\log r|^d)$ when $r$ goes to $0$. For each connected component of the space of real-analytic Anosov diffeomorphisms on a real-analytic manifold, we prove a dichotomy: either the exponent $d$ in our bound is never optimal, or it is optimal on a dense subset. Using examples constructed by Bandtlow, Just and Slipantschuk, we see that we are always in the latter situation for connected components of the space of real-analytic Anosov diffeomorphisms on the $2$-dimensional torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09881 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms Jézéquel, Malo Dynamical Systems 37C30, 37D20 We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension $d$, the number of resonances larger than $r$ is a $\mathcal{O}(|\log r|^d)$ when $r$ goes to $0$. For each connected component of the space of real-analytic Anosov diffeomorphisms on a real-analytic manifold, we prove a dichotomy: either the exponent $d$ in our bound is never optimal, or it is optimal on a dense subset. Using examples constructed by Bandtlow, Just and Slipantschuk, we see that we are always in the latter situation for connected components of the space of real-analytic Anosov diffeomorphisms on the $2$-dimensional torus. |
| title | Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms |
| topic | Dynamical Systems 37C30, 37D20 |
| url | https://arxiv.org/abs/2212.09881 |