Abstract:

We study dynamical behaviour of points in the boundaries of simply connected Baker domains $U$ for meromorphic maps $f$, such that $f$ has finite degree on $U$. We prove that if $f|_U$ is of hyperbolic or simply parabolic type, then almost every point in the boundary of $U$ with respect to harmonic measure escapes to infinity under iteration. On the contrary, if $f|_U$ is of doubly parabolic type, then almost every point in the boundary of $U$ with respect to harmonic measure is recurrent and, in particular, the set of escaping points in the boundary of $U$ has harmonic measure zero.

This is a joint work with K. Barasnki, N. Fagella and B. Karpinska