Han Peters: Wandering Fatou components for polynomial maps in 2 variables
Title: Wandering Fatou components for polynomial maps in 2 variables.
Abstract: The Fatou set of a holomorphic map is the largest open set on which the family of iterates is locally equicontinuous. The Fatou set is invariant and connected components are mapped onto connected components. In 1985 Dennis Sullivan proved that there are no wandering Fatou components for rational functions, meaning that every component is eventually mapped onto a periodic component. This completed the characterization of Fatou components on the Riemann sphere. Sullivan's proof makes use of quasiconformal deformations and can clearly not be generalized to higher dimensions. In this talk we will see that there exist polynomial maps in two complex variables that do have wandering Fatou components. This is join work with Matthieu Astorg, Xavier Buff, Romain Dujardin and Jasmin Raissy. We follow a suggestion of Misha Lyubich to apply the theory of parabolic implosion to polynomial skew-products.
Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!
Vodji seminarja
Josip Globevnik in Franc Forstnerič
