Title :

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

Author(s) :

Flaminio, Livio [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ravotti, Davide [Auteur]

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 >

Language :

Anglais

Comment :

24 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL