Fatou components and singularities of meromorphic functions
We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wand...
| Autores: | ; ; ; |
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| Tipo de documento: | Artigo |
| Estado: | Accepted version |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/130195 |
| Acesso em linha: | https://hdl.handle.net/2445/130195 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
| Resumo: | We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates $U_n$ of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values $p_n$ such that $\dist(p_n, U_n)\to 0$ as $n\to \infty$. We also prove that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a positive distance from the Julia set (in $\C$), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values. |
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