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Israel Journal of Mathematics

, Volume 210, Issue 1, pp 467–507 | Cite as

Mixing of frame flow for rank one locally symmetric spaces and measure classification

  • Dale WinterEmail author
Article

Abstract

Let G be a connected simple linear Lie group of rank one, and let Γ < G be a discrete Zariski dense subgroup admitting a finite Bowen-Margulis-Sullivan measure m BMS. We show that the right translation action of the one-dimensional diagonalizable subgroup is mixing on (Γ\G, m BMS). Together with the work of Roblin, this proves ergodicity of the Burger-Roblin measure under the horospherical group N, establishes a classification theorem for N invariant Radon measures on Γ\G, and provides precise asymptotics for the Haar measure matrix coefficients.

Keywords

Symmetric Space Haar Measure Transitivity Group Length Spectrum Duke Mathematical Journal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.ProvidenceUSA

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