Julia set of the function \(z\text{ exp}(z+\mu)\). II
type: Item
instance of: scholarly article
title: Julia set of the function \(z\text{ exp}(z+\mu)\). II
zbMATH Open document ID: 0896.30022
author: Tadashi Kuroda
author: Cheol Min Jang
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1998-07-08T00:00:00Z
review text: Continuing an earlier investigation by the second author [Tôhoku Math. J. II. Ser. 44, No. 2, 271-277 (1992; Zbl 0795.30022)], the paper studies the Julia set \(J(f)\) of the function \(f(z) =z \exp(z+ \mu)\), where \(\mu\) is a real parameter not less than 1. In particular there is shown to be a sequence \(\mu_n\), which tends to \(\infty\) as \(n\to\infty\), such that when \(\mu= \mu_n\) the orbit of the critical point \(-1\) is absorbed by a repelling fixed point of \(f\) and consequently \(J(f)= \mathbb{C}\). Some further values of \(\mu\) are found for which \(J(f)= \mathbb{C}\), using repelling cycles of higher order.
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 1140490
zbMATH Keywords: entire function
zbMATH Keywords: Julia set
Wikidata QID: Q123332835
reviewed by: I. N. Baker
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225063
OpenAlex ID: W2084360602
cites work: Q5593934
cites work: Dynamical properties of some classes of entire functions
cites work: Julia set of the function \(z\exp(z+\mu)\)
cites work: Q3036339
DOI: 10.2748/TMJ/1178225063
description: scientific article; zbMATH DE number 1140490