The bifurcation measure has maximal entropy

Date
2018/06/29 Fri 14:00 - 17:00
Room
6号館609号室
Speaker
Gabriel Vigny
Affiliation
Université de Picardie Jules Verne
Abstract

Consider a holomorphic family of rational maps of the Riemann sphere of degree d>1. We define a natural notion of entropy of bifurcation, mimicking the classical definition of entropy, by the parametric growth rate of critical orbits. We also define a notion a measure-theoretic bifurcation entropy for which we prove a variational principle: the measure of bifurcation is a measure of maximal entropy (joint work with De Thélin and Gauthier).