Measure of maximal entropy for minimal Anosov actions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909559247863808 |
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| author | Humbert, Tristan |
| author_facet | Humbert, Tristan |
| contents | For a minimal Anosov $\mathbb R^κ$-action on a closed manifold, we study the measure of maximal entropy constructed by Carrasco and Rodriguez-Hertz in \cite{CarHer} and show that it fits into the theory of Ruelle-Taylor resonances introduced by Guedes Bonthonneau, Guillarmou, Hilgert, and Weich in \cite{GBGHW}. More precisely, we show that the topological entropy corresponds to the first Ruelle-Taylor resonance for the action on a certain bundle of forms and that the measure of maximal entropy can be retrieved as the distributional product of the corresponding resonant and co-resonant states. As a consequence, we prove a Bowen-type formula for the measure of maximal entropy and a counting result on the number of periodic torii. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measure of maximal entropy for minimal Anosov actions Humbert, Tristan Dynamical Systems For a minimal Anosov $\mathbb R^κ$-action on a closed manifold, we study the measure of maximal entropy constructed by Carrasco and Rodriguez-Hertz in \cite{CarHer} and show that it fits into the theory of Ruelle-Taylor resonances introduced by Guedes Bonthonneau, Guillarmou, Hilgert, and Weich in \cite{GBGHW}. More precisely, we show that the topological entropy corresponds to the first Ruelle-Taylor resonance for the action on a certain bundle of forms and that the measure of maximal entropy can be retrieved as the distributional product of the corresponding resonant and co-resonant states. As a consequence, we prove a Bowen-type formula for the measure of maximal entropy and a counting result on the number of periodic torii. |
| title | Measure of maximal entropy for minimal Anosov actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.03457 |