Home > Articles > Published articles > Hyperbolic entire functions with bounded Fatou components |
Date: | 2015 |
Abstract: | 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. |
Grants: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Economía y Competitividad MTM2011-26995-C02-02 |
Note: | Agraïments: The third author was supported by a Philip Leverhulme Prize. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | 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 |
Published in: | Commentarii Mathematici Helvetici. A Journal of the Swiss Mathematical Society, Vol. 90 Núm. 4 (2015) , p. 799-829, ISSN 0010-2571 |
Postprint 27 p, 2.8 MB |