On infinite area for complex exponential function
type: Item
instance of: scholarly article
title: On infinite area for complex exponential function
zbMATH Open document ID: 1063.30026
author: Figen Çilingir
published in: Chaos, Solitons and Fractals
publication date: 2005-03-08T00:00:00Z
review text: This article discusses (relaxed) Newton's method as applied to the two functions \(z\exp(z)\) and \(z\exp(z^2)\). The result is that the attracting basin of the root \(z=0\) has infinite area in both cases. The paper contains many computer pictures of the attracting domains, unfortunately labelled as ``red'' and ``purple'' but printed in grey; the colored versions can be found online. Here are some updates on the cited references: \textit{D. S. Alexander}'s thesis of 1992 cited as [1] has appeared in 1994 in book form ``A history of complex dynamics. From Schröder to Fatou and Julia (1994; Zbl 0788.30001), and Sutherland's 1990 preprint cited as [13] has appeared in 2001 [\textit{J. Hubbard}, the reviewer and \textit{S. Sutherland}, Invent. Math. 146, No. 1, 1--33 (2001; Zbl 1048.37046)].
reviewed by: Dierk Schleicher
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 2141662
zbMATH Keywords: relaxed Newton's method
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.04.031
OpenAlex ID: W2049886235
cites work: Q4002072
cites work: Invariant sets under iteration of rational functions
cites work: On the iteration of a rational function: Computer experiments with Newton's method
cites work: FINITENESS OF THE AREA OF BASINS OF ATTRACTION OF RELAXED NEWTON METHOD FOR CERTAIN HOLOMORPHIC FUNCTIONS
cites work: Newton's method and complex dynamical systems
cites work: Multiple attractors in Newton's method
cites work: Newton’s Algorithm and Chaotic Dynamical Systems
cites work: Q4264327
DOI: 10.1016/J.CHAOS.2004.04.031
description: scientific article; zbMATH DE number 2141662