For a family of rational maps, results by Lyubich, Mané-Sad-Sullivan and DeMarco provide a fairly complete understanding of dynamical stability. I will review this one-dimensional theory and present a recent generalisation to several complex variables. I will focus on the arguments that do not readily generalise to this setting, and introduce the tools and ideas that allow one to overcome these problems.
Holomorphic motions of Julia sets
Fabrizio Bianchi (Imperial College)
Tue, 26/09/2017 - 16:00