# Holomorphic Motions and their applications to holomorphic dynamics

Dates:
19.02.04 - 19.05.04
Place:
Barcelona, Spain
Organizers:
Núria Fagella

#### Main Speaker

Christian Henriksen (Technical University of Denmark)

#### Abstract

The theory of holomorphic motions has many applications to holomorphic dynamics, quasiconformal mappings, Teichmûller theory and the interplay between them. Mañé, Sad and Sullivan invented the notion of a holomorphic motion as a tool of investigating holomorphic dynamical systems in the eighties, and it was the applications to dynamical systems that initially motivated the development of the theory. However, since then the theory has become a subfield of complex analysis in its own right and can be studied without any reference to dynamics.  While the study of holomorphic motions can be cut away from its roots in dynamics, this is not what we intend to do in this seminar. Here we will see how holomorphic motions provide a bridge from quasiconformal mappings and Teichmûller theory to their applications in dynamical systems. Time permitting, we will conclude by sketching a proof of the extended $\lambda$-lemma of Slodkowsky.