Isometric extensions of Anosov flows via microlocal analysis
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913280055836672 |
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| author | Lefeuvre, Thibault |
| author_facet | Lefeuvre, Thibault |
| contents | We revisit the classical framework developed by Brin, Pesin and others to study ergodicity and mixing properties of isometric extensions of volume-preserving Anosov flows, using the microlocal framework developed in the theory of Pollicott-Ruelle resonances. The approach developed in the present note is reinvested in the companion paper [arXiv:2111.14811] in order to show ergodicity of the frame flow on negatively-curved Riemannian manifolds under nearly $1/4$-pinched curvature assumption (resp. nearly $1/2$-pinched) in dimension $4$ and $4\ell+2, \ell > 0$ (resp. dimension $4\ell, \ell > 0$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_05979 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Isometric extensions of Anosov flows via microlocal analysis Lefeuvre, Thibault Dynamical Systems Analysis of PDEs Differential Geometry 37A05, 37A25, 37A30, 37D40, 35A27 We revisit the classical framework developed by Brin, Pesin and others to study ergodicity and mixing properties of isometric extensions of volume-preserving Anosov flows, using the microlocal framework developed in the theory of Pollicott-Ruelle resonances. The approach developed in the present note is reinvested in the companion paper [arXiv:2111.14811] in order to show ergodicity of the frame flow on negatively-curved Riemannian manifolds under nearly $1/4$-pinched curvature assumption (resp. nearly $1/2$-pinched) in dimension $4$ and $4\ell+2, \ell > 0$ (resp. dimension $4\ell, \ell > 0$). |
| title | Isometric extensions of Anosov flows via microlocal analysis |
| topic | Dynamical Systems Analysis of PDEs Differential Geometry 37A05, 37A25, 37A30, 37D40, 35A27 |
| url | https://arxiv.org/abs/2112.05979 |