Friday December 9th, 2022 | |
| Time: | 2:30 PM |
| Title: | Regular and stochastic properties of the maximal entropy measure on CP(k), k=1,2. |
| Speaker: | Christophe Dupont, Universite de Rennes 1 |
| Location: | Math P-131 |
| Abstract: | |
| A rational map of degree d > 1 on CP(1) has a unique measure of maximal entropy mu. Its Lyapunov exponent lambda is bounded below by (1/2) log d and its dimension m is equal to log d / lambda. Moreover, mu is absolutely continuous with respect to the m-Hausdorff measure if and only if f is a power, Tchebichev or Lattès map. This rigidity result, due to Zdunik, relies on stochastic properties for mu, provided by the convergence of a geometric coding tree, worked out by Przytycki-Urbanski-Zdunik. In this talk, we shall review counterpart results for holomorphic mappings on CP(2) (which are no more conformal) and discuss open problems in this context. | |