# H\"older regularity for the spectrum of translation flows

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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02438996
Contributor : Sergey Berezin <>
Submitted on : Tuesday, January 14, 2020 - 2:13:57 PM
Last modification on : Thursday, January 23, 2020 - 6:22:13 PM

### Identifiers

• HAL Id : hal-02438996, version 1
• ARXIV : 1908.09347

### Citation

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

Record views