Proximality and equidistribution on the Furstenberg boundary

2004/06/10 by A. Gorodnik, Gorodnik, A., F. Maucourant +1
Mathematics · #22E40 #37A17 #57S30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:22E40 #msc:37A17 #msc:57S30

paper · pdf · doi:10.48550/arxiv.math/0406219

arxiv created 2004/06/10 · arxiv updated 2009/12/01

Abstract

Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Γa lattice in G. We prove that every Γ-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Γon G/P.

Related

• Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
• Lattice action on the boundary of SL(n,R)
• Finitary estimates for the distribution of lattice orbits in homogeneous spaces I: Riemannian metric
• Equidistribution and measure rigidity under × p,× q
• Projections from Furstenberg boundaries onto maximal flats and barycenter maps