Abelian covers of hyperbolic surfaces: ...
Document type :
Pré-publication ou Document de travail
Title :
Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows
Author(s) :
Publication date :
2022-07-17
HAL domain(s) :
Mathématiques [math]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Comment :
24 pages
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