Abelian covers of hyperbolic surfaces: ...
Type de document :
Pré-publication ou Document de travail
Titre :
Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows
Auteur(s) :
Date de publication :
2022-07-17
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Commentaire :
24 pages
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