The denotations of Julia sets of transcendental entire functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0984.30016
author: Lingmei Zhu
author: Yuansheng Bao
author: Xiaoling Wang
publication date: 2002-04-21T00:00:00Z
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37F10
zbMATH DE Number: 1616451
zbMATH Keywords: Fatou set
zbMATH Keywords: Julia set
zbMATH Keywords: entire function
zbMATH Keywords: Fatou exceptional value
MaRDI profile type: Publication
title: The denotations of Julia sets of transcendental entire functions
published in: Journal of Nanjing University. Mathematical Biquarterly
review text: Let \(f\) be an entire transcendental function, \(F(f)\) its Fatou set and \(J(f)\) its Julia set. Then \(J(f)\subset\overline{\bigcup^{\infty}_{n=0}f^{-n}(a)}\) if \(a\in{\mathbb C}\) is not a Fatou exceptional value. If \(a\in J(f)\), then we have equality. The authors claim that we have equality also for certain \(a\in F(f)\). As \(\bigcup^{\infty}_{n=0}f^{-n}(a)\subset F(f)\) for \(a\in F(f)\) by the complete invariance of \(F(f)\), this statement seems to be false.
reviewed by: Walter Bergweiler
description: scientific article; zbMATH DE number 1616451