On the dynamics of a family of singularly perturbed rational maps
type: Item
instance of: scholarly article
title: On the dynamics of a family of singularly perturbed rational maps
zbMATH Open document ID: 1321.37046
author: Fei Yang
author: JianXun Fu
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-12-19T00:00:00Z
review text: The authors study the rational map \(z_{j+1}=f(z_j)\) with \(f(z)=z^n(z^{2n}-\lambda^{n+1})/(z^{2n}-\lambda^{3n-1})\), where \(n>1,\lambda\neq 0\) and \(\lambda^{2n-2}\neq 1\). This map can be thought of as a perturbation of the map \(z_{j+1}=z_j^n\) and in that sense is similar to the McMullen map \(f_M(z)=z^n+\lambda/z^d\). The main result is the determination of conditions under which the Julia set of \(f\) is (i) a quasicircle, (ii) a Cantor set of circles, (iii) a Sierpinski carpet, (iv) a degenerated Sierpinski carpet.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 6381769
zbMATH Keywords: Julia set
zbMATH Keywords: Cantor circles
zbMATH Keywords: Sierpinski carpet
zbMATH Keywords: singular perturbation
reviewed by: Carlo Laing
MaRDI profile type: Publication
full work available at URL: j.jmaa.2014.10.090
OpenAlex ID: W1985245097
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DOI: 10.1016/J.JMAA.2014.10.090
description: scientific article; zbMATH DE number 6381769