In this talk, we will discuss the dynamics on the boundaries of Baker domains of entire functions.
By definition, points in the interior of a Baker domain converge to infinity through the
so-called dynamical access. In its boundary, dynamics are wilder. In particular, one can ask
whether there are points on the boundary which converge to infinity under iteration, and, more
precisely, if there are points which converge to infinity through the dynamical access.
Both questions are intimately related with the boundary behavior of the inner function
associated with the Baker domain by the Riemann map. The purpose of this talk is to try to answer
the previous questions for the different types of Baker domains.
This is based on joint work with Prof. N. Fagella.