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Title: Accesses to infinity from Fatou components.
Author: Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
Keywords: Funcions meromorfes
Sistemes dinàmics complexos
Meromorphic functions
Complex dynamical systems
Issue Date: 2017
Publisher: American Mathematical Society (AMS)
Abstract: We study the boundary behaviour of a meromorphic map $f\mathbb{C} \rightarrow \widehat{C}$ on its invariant simply connected Fatou component $U$. To this aim, we develop the theory of accesses to boundary points of $U$ and their relation to the dynamics of $f$. In particular, we establish a correspondence between invariant accesses from $U$ to infinity or weakly repelling points of $f$ and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps.
Note: Versió postprint del document publicat a:
It is part of: Transactions of the American Mathematical Society, 2017, vol. 369, num. 3, p. 1835-1867
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ISSN: 0002-9947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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