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

2022/07/17 by Livio Flaminio, Flaminio, Livio, Davide Ravotti +1 · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometry and complex manifolds #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2207.08263

Abstract

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on ℤ^d-covers, thus proving a strong form of Krickeberg mixing. 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.

Cited by

• K-mixing for aperiodic Lorentz gases
• Mixing asymptotics for time-changes of horocycle flows

Related

• Horocycle flows on abelian covers of surfaces of negative curvature
• Local mixing and invariant measures for horospherical subgroups on abelian covers
• Local mixing on abelian covers of hyperbolic surfaces with cusps
• Time-Changes of Horocycle Flows
• Joining measures for horocycle flows on abelian covers