9 may 2016 -- 14:30
Aula Tricerri, DiMaI, Firenze
INdAM Intensive Period "Hypercomplex Function Theory and Applications"
Abstract.
In order to study the forward or backward iteration of a holomorphic self-map $f$ of a complex manifold $X$, it is natural to search for a semi-conjugacy of $f$ with some automorphism of a complex manifold. Examples of this approach are given by the Schroeder, Valiron and Abel equation in the unit disc $D$. Given a holomorphic self-map $f$ of the ball $B^q$, we show that it is canonically semi-conjugate to an automorphism (called a canonical model) of a possibly lower dimensional ball $B^k$, and this semi-conjugacy satisfies a universal property. This approach unifies in a common framework recent works of Bracci, Gentili, Poggi-Corradini, Ostapyuk.