Baranski, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavierKarpinska, Boguslawa2020-06-032020-12-3120190021-7670https://hdl.handle.net/2445/164077We 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.28 p.application/pdfeng(c) Springer, 2019Funcions de variables complexesSistemes dinàmics complexosFuncions meromorfesFunctions of complex variablesComplex dynamical systemsMeromorphic functionsinfo:eu-repo/semantics/article6702462020-06-03info:eu-repo/semantics/openAccess