Dynamics Seminar

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

Thursday, April 18, 2024 - 2:55pm
Malott 206

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 reveals a dimension jump under perturbation, which is a local generalization of Bowen's dimension rigidity result. The core of the proof is to study the stationary measures of finitely supported random walks on SL(3,R). We show the Hausdorff dimensions of the measures are equal to their Lyapunov dimensions under certain assumptions. This is based on the joint works with Jialun Li, Yuxiang Jiao and Disheng Xu.