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Hölder regularity for the spectrum of translation flows

Abstract : The paper is devoted to generic translation flows corresponding to Abelian dif-ferentials on flat surfaces of arbitrary genusg>2. These flows are weakly mixing by theAvila-Forni theorem. In genus2, the Hölder property for the spectral measures of these flowswas established in [12, 14]. Recently, Forni [18], motivated by [12], obtained Hölder estimatesfor spectral measures in the case of surfaces of arbitrary genus. Here we combine Forni’s ideawith the symbolic approach of [12] and prove Hölder regularity for spectral measures of flowson random Markov compacta, in particular, for translation flows for an arbitrary genus>2
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Contributor : Julien Caugant <>
Submitted on : Monday, August 30, 2021 - 5:02:40 PM
Last modification on : Tuesday, August 31, 2021 - 3:26:56 AM

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Alexander Bufetov, Boris Solomyak. Hölder regularity for the spectrum of translation flows. Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021, 8, pp.279 - 310. ⟨10.5802/jep.146⟩. ⟨hal-03329195⟩

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