Uniqueness of conformal measures and local mixing for Anosov groups

2021/11/24 by Edwards, Sam, Lee, Minju, Oh, Hee · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2111.12752

Abstract

In the late seventies, Sullivan showed that for a convex cocompact subgroup Γ of SO^∘(n,1) with critical exponent δ>0, any Γ-conformal measure on ∂ ℍⁿ of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on Γ\backslash G including Haar measures.

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