H\"older regularity for the spectrum of translation flows

Alexander I. Bufetov (1) , Boris Solomyak (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics [Ramat Gan]

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.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

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