Joint partial equidistribution of Farey rays in negatively curved manifolds and trees

Abstract

We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial equidistribution of Farey fractions at a given density, and give several analogous arithmetic applications, including in Bruhat-Tits trees.

36 pages. Some modifications in the introduction and additional references

References in corpus (5)

• Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
• The Asymptotic distribution of circles in the orbits of Kleinian groups
• Effective Limit Distribution of the Frobenius Numbers
• Counting common perpendicular arcs in negative curvature
• Skinning measures in negative curvature and equidistribution of equidistant submanifolds