16/04/2012. Introduction to Theory of Prime Ends
18/04/2012. Applications I: Index of iterates of planar homeomorphisms
20/04/2012. Applications II: Rotation number of planar attractors
Abstract: Let U be a simply connected proper open set of the 2-sphere. While U is homeomorphic to the open disk, the boundary of U may have a very complicated topological structure. Carathéodory’s prime ends compactification allows one to compactify U, by adding the set of prime ends, in such a way that one obtains a closed disk. We will explain in a intuitive way how this compactification works and some applications to planar dynamics.