Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms
| Autor: | Jézéquel, Malo |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: v2: Revision according to referee comments |
| Databáze: | arXiv |
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