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Absorbing sets and Baker domains for holomorphic maps

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We consider holomorphic maps $f: U \rightarrow U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice absorbing domains $W \subset U$. In this paper we show that $W$ can be chosen to be simply connected, if $f$ has doubly parabolic type in the sense of the Baker-Pommerenke-Cowen classification of its lift by a universal covering (and $\zeta$ is not an isolated boundary point of $U$). We also provide counterexamples for other types of the map $f$ and give an exact characterization of doubly parabolic type in terms of the dynamical behaviour of $f$.

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Journal of the London Mathematical Society-Second Series, 2015, vol. 92, num. 1, p. 144-162

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Absorbing sets and Baker domains for holomorphic maps