On the dimension of limit sets on the real projective plane via stationary measures

Speaker. Jialun Li
Date. 12.09.23 at 16:00

Abstract. I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the affinity dimension. In particular, it exhibits a dimension jump under perturbation.
The key tool is to study the stationary measures of finitely supported random walks on SL(3,R). We show the Hausdorff dimensions equal the Lyapunov dimensions under certain assumption. This is based on an ongoing joint work with Wenyu Pan and Disheng Xu.