A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913364758757376 |
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| author | Galli, Daniele |
| author_facet | Galli, Daniele |
| contents | We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham cohomology. We finally exploit this relation to get information about the Ruelle-Pollicott asymptotics of the correlation function and establish a cohomological bound for the speed of mixing of Anosov diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms Galli, Daniele Dynamical Systems Differential Geometry 37A25, 37D20 (Primary), 37C30 (Secondary), 14F40 We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham cohomology. We finally exploit this relation to get information about the Ruelle-Pollicott asymptotics of the correlation function and establish a cohomological bound for the speed of mixing of Anosov diffeomorphisms. |
| title | A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms |
| topic | Dynamical Systems Differential Geometry 37A25, 37D20 (Primary), 37C30 (Secondary), 14F40 |
| url | https://arxiv.org/abs/2405.17045 |