Hyperbolic entire functions with bounded Fatou components
We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:169433 |
| Acesso em linha: | https://ddd.uab.cat/record/169433 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Axiom A Bounded Fatou component Eremenko-Lyubich class Fatou set Hyperbolicity Jordan curve Julia set Laguerre-Pólya class Local connectivity Quasicircle Quasidisc Transcendental entire function |
| Resumo: | We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values. |
|---|