# Accesses to infinity from Fatou components

Date:
24.11.14
Times:
15:30 to 16:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Núria Fagella
University:
UB

#### Abstract:

We study the boundary behaviour of a meromorphic transcendental map $f:C \longrightarrow\widehat{C}$ on an invariant simply connected Fatou component $U$. To this aim, we develop the theory of accesses to boundary points of $U$ and their relation to the dynamics of $f$. In particular, we establish a correspondence between invariant accesses from $U$ to infinity, weakly repelling points of $f$ and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps applied to entire transcendental functions.