Dynamical Systems Seminar - Holomorphic motions of Julia sets: dynamical stability in one and several complex variables

Speaker: Fabrizio Bianchi  (Laboratoire Paul Painlev, Lille)

Abstract: In this talk we discuss stability of holomorphic dynamical systems under perturbation. In dimension 1, the theory is now classical and is based on works by Lyubich, Mané-Sad-Sullivan and DeMarco. I will review this theory and present a recent generalization valid in any dimension. Since classical 1-dimensional techniques no longer apply in higher dimensions, our approach is based on ergodic and pluripotential methods.