On asymptotic expansions of ergodic integrals for $\Z^d$-extensions of translation flows
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916686851997696 |
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| author | Bruin, Henk Fougeron, Charles Ravotti, Davide Terhesiu, Dalia |
| author_facet | Bruin, Henk Fougeron, Charles Ravotti, Davide Terhesiu, Dalia |
| contents | We obtain expansions of ergodic integrals for $\Z^d$-covers of compact self-similar translation flows, and as a consequence we obtain a form of weak rational ergodicity with optimal rates. As examples, we consider the so-called self-similar $(s,1)$-staircase flows ($\Z$-extensions of self-similar translations flows of genus-$2$ surfaces), and particular cases of the Ehrenfest wind-tree model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On asymptotic expansions of ergodic integrals for $\Z^d$-extensions of translation flows Bruin, Henk Fougeron, Charles Ravotti, Davide Terhesiu, Dalia Dynamical Systems Primary 37E35, Secondary 28D05, 37H05, 14H30, 60F15 We obtain expansions of ergodic integrals for $\Z^d$-covers of compact self-similar translation flows, and as a consequence we obtain a form of weak rational ergodicity with optimal rates. As examples, we consider the so-called self-similar $(s,1)$-staircase flows ($\Z$-extensions of self-similar translations flows of genus-$2$ surfaces), and particular cases of the Ehrenfest wind-tree model. |
| title | On asymptotic expansions of ergodic integrals for $\Z^d$-extensions of translation flows |
| topic | Dynamical Systems Primary 37E35, Secondary 28D05, 37H05, 14H30, 60F15 |
| url | https://arxiv.org/abs/2402.02266 |