Please use this identifier to cite or link to this item:
Title: Hyperbolic entire functions with bounded Fatou components
Author: Bergweiler, Walter
Fagella Rabionet, Núria
Rempe-Gillen, Lasse
Keywords: Sistemes dinàmics complexos
Funcions de variables complexes
Complex dynamical systems
Functions of complex variables
Issue Date: 12-Mar-2015
Publisher: Springer Verlag
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.
Note: Versió postprint del document publicat a:
It is part of: Commentarii Mathematici Helvetici, 2015, vol. 90, num. 4, p. 799-829
Related resource:
ISSN: 0010-2571
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
660986.pdf2.99 MBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.