Homin Lee: Random dynamics on surfaces

Abstract: In this talk, we will discuss about smooth random dynamical systems and group actions on surfaces. When a group action on torus is given by toral automorphisms, Benoist-Quint classified orbit closures (and stationary measures), using random dynamics. In this talk, we will study group actions that are given by diffeomorphisms, using random dynamics. We will discuss about absolutely continuity of stationary measures, classification of orbit closure, and exact dimensionality of stationary measures. This talk will be mostly about an ongoing work with Aaron Brown, Davi Obata, and Yuping Ruan.