Accesses to infinity from Fatou components.
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 correspo...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/164087 |
| Acesso em linha: | https://hdl.handle.net/2445/164087 |
| Access Level: | acceso abierto |
| Palavra-chave: | Funcions meromorfes Sistemes dinàmics complexos Meromorphic functions Complex dynamical systems |
| Resumo: | 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. |
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