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http://hdl.handle.net/2445/164077
Title: | Escaping points in the boundaries of baker domains |
Author: | Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
Keywords: | Funcions de variables complexes Sistemes dinàmics complexos Funcions meromorfes Functions of complex variables Complex dynamical systems Meromorphic functions |
Issue Date: | 2019 |
Publisher: | Springer |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s11854-019-0011-0 |
It is part of: | Journal d'Analyse Mathematique, 2019, vol. 137, num. 2, p. 679-706 |
URI: | http://hdl.handle.net/2445/164077 |
Related resource: | https://doi.org/10.1007/s11854-019-0011-0 |
ISSN: | 0021-7670 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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