Renormalization of Unicritical Diffeomorphisms of the Disk

Speaker. Jonguk Yang
Date. 19.12.23 at 16:00

Abstract. Critical points play a crucial role in 1D dynamical systems as natural sources of non-linearity. They allow seemingly simple maps to have extremely rich and complicated behaviors.
One of the simplest settings in which one can study the dynamical effects of critical points is the class of unimodal interval maps. The dynamics of these maps is now very well understood, due to the celebrated renormalization theory of Sullivan, McMullen, Lyubich and Avila.
The goal of this talk is to generalize this theory to a two-dimensional setting: namely, to dissipative diffeomorphisms of the disk. I will identify the notion of “2D unicriticality,” and then give a survey of our main results (including renormalization convergence). Time permitting, I will also describe the dynamical structure of 2D unicritical systems using what we call “a unicritical cover.”

This talk is based on a joint work with S. Crovisier, M. Lyubich and E. Pujals.