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arXiv · 1908.09347

H\"older regularity for the spectrum of translation flows

Alexander I. Bufetov·Boris Solomyak
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Abstract

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 H\"older property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained H\"older 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 H\"older regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera.

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Alexander I. Bufetov, Boris Solomyak. 2019-08-25. H\"older regularity for the spectrum of translation flows. https://arxiv.org/abs/1908.09347

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