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| Main Authors: | , |
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| Format: | Preprint |
| Udgivet: |
2019
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| Fag: | |
| Online adgang: | https://arxiv.org/abs/1908.09347 |
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Indholdsfortegnelse:
- 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.