Growth conditions for entire functions with only bounded Fatou components
type: Item
instance of: scholarly article
title: Growth conditions for entire functions with only bounded Fatou components
zbMATH Open document ID: 1183.30021
author: Aimo Hinkkanen
author: Joseph Miles
published in: Journal d'Analyse Mathématique
publication date: 2009-11-02T00:00:00Z
review text: In this paper among others the following result is proved. Theorem: Let \(f\) be a transcendental entire function of order less than \(1/2\). Suppose that there exists \(\alpha> 1\), \(R_0> 1\), and a positive decreasing function \(\gamma(r)\) such that for every \(R> R_0\), there exists \(r\in(R,R^\alpha]\) with \[ {\log m(r,f)\over \log M(R,f)}\geq \alpha(1- \gamma(R)) \] and \(\sum_n \gamma(e^{2n})<\infty\). Then all components of the Fatou set of \(f\) are bounded. Some other interesting results concerning Fatou sets for entire function are obtained.
reviewed by: Jan Stankiewicz
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 30D20
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 5624017
zbMATH Keywords: Fatou component
zbMATH Keywords: growth condition
zbMATH Keywords: entire function
MaRDI profile type: Publication
full work available at URL: s11854-009-0019-y
OpenAlex ID: W2063465672
cites work: Unbounded domains of normality
cites work: Q3929977
cites work: Wandering Domains in the Iteration of Entire Functions
cites work: Q4002072
cites work: Complex dynamics
cites work: Q3365956
cites work: Q3530534
cites work: AN EXTREMAL PROBLEM IN VALUE-DISTRIBUTION THEORY
cites work: Q4264327
cites work: Functions of small growth with no unbounded Fatou components
cites work: The Hausdorff dimension of Julia sets of entire functions
cites work: The iteration of entire functions of small growth
cites work: Rational iteration: complex analytic dynamical systems
cites work: Unbounded domains of normality of entire functions of small growth
DOI: 10.1007/S11854-009-0019-Y
description: scientific article; zbMATH DE number 5624017