Files
Document type
ArticleVersion
Accepted versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164120
Hyperbolic entire functions with bounded Fatou components
Journal Title
Director/Tutor
Additional contribution
Journal ISSN
Volume Title
Abstract
We show that an invariant Fatou component of a hyperbolic transcenden- tal 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 re- sults are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.
Related resource
Subject (English)
Citation
Citation
BERGWEILER, Walter, FAGELLA RABIONET, Núria and REMPE-GILLEN, Lasse. Hyperbolic entire functions with bounded Fatou components. Commentarii Mathematici Helvetici. 2015. Vol. 90, num. 4, pags. 799-829. ISSN 0010-2571. [consulted: 6 of October of 2026]. Available at: https://hdl.handle.net/2445/164120