Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces
For convex cocompact (and more generally, geometrically finite) rank one locally symmetric spaces, Winter proved mixing of the frame flow with respect to the Bowen-Margulis-Sullivan measure. Mixing results in homogeneous dynamics have many applications in counting, equidistribution, and decay of matrix coefficients. For Anosov subgroups of higher rank Lie groups, the analogous Bowen-Margulis-Sullivan measures are infinite and one looks for local mixing. In a joint work with Michael Chow, we prove local mixing of one-parameter diagonal flows on Anosov homogeneous spaces, generalizing the result of Winter. We also discuss some applications including a recent result of Chow-Fromm regarding joint equidistribution of maximal flat cylinders and holonomies.