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

Jouni Parkkonen , Frédéric Paulin (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

Jouni Parkkonen, Frédéric Paulin. Joint partial equidistribution of Farey rays in negatively curved manifolds and trees. 2022. ⟨hal-03907491⟩