Hölder regularity for the spectrum of translation flows

Fuente: arXiv
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Autores principales: Bufetov, Alexander I., Solomyak, Boris
Formato: Preprint
Publicado: 2019
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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