Pré-Publication, Document De Travail Année : 2020

H\"older regularity for the spectrum of translation flows

Résumé

The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus g2. 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.

Dates et versions

hal-02438996 , version 1 (14-01-2020)

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Alexander I. Bufetov, Boris Solomyak. H\"older regularity for the spectrum of translation flows. 2020. ⟨hal-02438996⟩
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