Univalent wandering domains in the Eremenko-Lyubich class

We use the Folding Theorem of [Bis15] to construct an entire function $f$ in class $\mathcal{B}$ and a wandering domain $U$ of $f$ such that $f$ restricted to $f^{n}(U)$ is univalent, for all $n \geq 0$. The components of the wandering orbit are bounded and surrounded by the postcritical set.

Detalhes bibliográficos
Autores: Fagella Rabionet, Núria, Jarque i Ribera, Xavier, Lazebnik, Kirill
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2019
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164060
Acesso em linha:https://hdl.handle.net/2445/164060
Access Level:Acceso aberto
Palavra-chave:Funcions de variables complexes
Sistemes dinàmics complexos
Funcions meromorfes
Functions of complex variables
Complex dynamical systems
Meromorphic functions
Descrição
Resumo:We use the Folding Theorem of [Bis15] to construct an entire function $f$ in class $\mathcal{B}$ and a wandering domain $U$ of $f$ such that $f$ restricted to $f^{n}(U)$ is univalent, for all $n \geq 0$. The components of the wandering orbit are bounded and surrounded by the postcritical set.