Unstable entropy for Anosov diffeomorphisms on the 3-torus
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912772299685888 |
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| author | Humbert, Tristan |
| author_facet | Humbert, Tristan |
| contents | For Anosov diffeomorphisms on the $3$-torus which are strongly partially hyperbolic with expanding center, we construct systems of strong unstable and center stable Margulis measures which are holonomy-invariant. This allows us to obtain a characterization of the measures of maximal unstable entropy in terms of their conditional measures along the strong unstable leaves. Moreover, we show that the Margulis systems identify with Pollicott-Ruelle (co)-resonant states for the action on 2-forms. This shows that the unstable topological entropy and a measure of maximal unstable entropy can be retrieved from the spectral approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unstable entropy for Anosov diffeomorphisms on the 3-torus Humbert, Tristan Dynamical Systems For Anosov diffeomorphisms on the $3$-torus which are strongly partially hyperbolic with expanding center, we construct systems of strong unstable and center stable Margulis measures which are holonomy-invariant. This allows us to obtain a characterization of the measures of maximal unstable entropy in terms of their conditional measures along the strong unstable leaves. Moreover, we show that the Margulis systems identify with Pollicott-Ruelle (co)-resonant states for the action on 2-forms. This shows that the unstable topological entropy and a measure of maximal unstable entropy can be retrieved from the spectral approach. |
| title | Unstable entropy for Anosov diffeomorphisms on the 3-torus |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.09520 |