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Pré-Publication, Document De Travail Année : 2022

Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows

Livio Flaminio
Davide Ravotti
  • Fonction : Auteur

Résumé

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on $\mathbb{Z}^d$-covers, thus proving a strong form of Krickeberg mixing. This is the first result on infinite mixing for parabolic flows. We also prove that the spectral measures around $0$ of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.

Dates et versions

hal-04404266 , version 1 (18-01-2024)

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Livio Flaminio, Davide Ravotti. Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows. 2024. ⟨hal-04404266⟩
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