# name
Escaping points in the boundaries of baker domains

# metadata.dc.description.abstract[].value
We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains $U$ of meromorphic maps $f$ with a 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 of $f$. 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, has dense forward trajectory in the boundary of $U$, in particular the set of escaping points in the boundary of $U$ has harmonic measure zero. We also present some extensions of the results to the case when $f$ has infinite degree on $U$, including classical Fatou example.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Escaping points in the boundaries of baker domains