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

By Dale Winter. 2014

59 citations recorded by the source corpus.

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 mBMS. We show that the right translation action of the one-dimensional diagonalizable subgroup is mixing on (Γ\G, mBMS). 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2543a0af89e283a3e5087284e42dc9d2a5fc6b5

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Anosov groups: local mixing, counting and equidistribution (2020, background): “4) WhenG has rank one, this was completely answered by Roblin and Winter ([48], [58]) for geometrically finite subgroups and by Oh and Pan [35] for co-abelian subgroups of convex cocompact subgroups.”
Geodesic planes in hyperbolic 3-manifolds (2016, background): “3 can also be based on ergodicity of the geodesic flow on the frame bundle for Zariski dense convex cocompact Kleinian groups, established in [30].”
Matrix coefficients, counting and primes for orbits of geometrically finite groups (2012, methodology): “The BMS measure mBMS on 0\G is known to be mixing for the frame flows ([18], [67]).”