Hölder regularity for the spectrum of translation flows
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866916082140315648 |
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| author | Bufetov, Alexander I. Solomyak, Boris |
| author_facet | Bufetov, Alexander I. Solomyak, Boris |
| contents | The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the Hölder property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained Hölder estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Forni's idea with the symbolic approach of [10] and prove Hölder regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_09347 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Hölder regularity for the spectrum of translation flows Bufetov, Alexander I. Solomyak, Boris Dynamical Systems 37Axx, 37Dxx The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the Hölder property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained Hölder estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Forni's idea with the symbolic approach of [10] and prove Hölder regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera. |
| title | Hölder regularity for the spectrum of translation flows |
| topic | Dynamical Systems 37Axx, 37Dxx |
| url | https://arxiv.org/abs/1908.09347 |