The case of equality in the dichotomy of Mohammadi-Oh

2017/01/17 by Dufloux, Laurent
#28A80 #37C45 #37D40 #53D25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.04555

Abstract

If n ≥ 3 and Γ is a convex-cocompact Zariski-dense discrete subgroup of SO^o(1,n+1) such that δ_Γ=n-m where m is an integer, 1 ≤ m ≤ n-1, we show that for any m-dimensional subgroup U in the horospheric group N, the Burger-Roblin measure associated to Γ on the quotient of the frame bundle is U-recurrent.

Related

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• Conformal measure rigidity and ergodicity of horospherical foliations