Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/164120
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: https://doi.org/10.4171/CMH/371 |
It is part of: | Commentarii Mathematici Helvetici, 2015, vol. 90, num. 4, p. 799-829 |
URI: | http://hdl.handle.net/2445/164120 |
Related resource: | https://doi.org/10.4171/CMH/371 |
ISSN: | 0010-2571 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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660986.pdf | 2.99 MB | Adobe PDF | View/Open |
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