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Escaping points in the boundaries of baker domains
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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.
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BARANSKI, Krzysztof, FAGELLA RABIONET, Núria, JARQUE I RIBERA, Xavier, KARPINSKA, Boguslawa. Escaping points in the boundaries of baker domains. _Journal d'Analyse Mathematique_. 2019. Vol. 137, núm. 2, pàgs. 679-706. [consulta: 25 de gener de 2026]. ISSN: 0021-7670. [Disponible a: https://hdl.handle.net/2445/164077]