|Date:||Wed, October 5, 2011|
|Place:||Research II Lecture Hall|
Abstract: We consider iteration problems for polynomial mappings in several complex variables. We say that a point x lies in the Fatou set if the orbits of points near x remain close to the orbit of x. A Fatou component is a connected component of the Fatou set. Roughly speaking the Fatou component containing x is the largest connected open set for which all orbits have the same asymptotical behavior as the orbit of x. In one complex variable Fatou components are very well understood. In higher dimensions this is not the case. I will give an overview of what is known for some classes of maps, and discuss recent work with Mikhael Lyubich.