Speaker：Yunping Jiang（The City University of New York）

Time：2021-07-08 10:00

Location：Tencent Meeting ID：566715784（No Password）

Abstract:

In this talk, I will mention a joint work with Huyi Hu and Miaohua Jiang on constructing smooth paths in the same type of Anosov or area preserving Anosov dynamical systems, which are in the space of Anosov and area preserving Blaschke products respectively. The metric entropy takes any value from zero+ to the topological entropy. The former tends to an almost Anosov Blaschke product which is smoothly conjugate to the famous Boole map, giving a new explanation of Boole's formula, and the latter tends to a totally degenerate map. These two paths represent the same smooth path in the space of all smooth conjugacy classes of Anosov Blaschke products, which enables me to prove a global graph of the metric entropy on such space and obtain a complete description of the shape of the metric entropy. Furthermore, I provide a global picture of the measure-theoretic entropy on the main cardioid of the Mandelbrot set for the Gibbs measures.