Dynamics of regularly ramified rational maps. I: Julia sets of maps in one-parameter families
type: Item
instance of: scholarly article
title: Dynamics of regularly ramified rational maps. I: Julia sets of maps in one-parameter families
zbMATH Open document ID: 1400.37051
author: Jun Hu
author: Oleg Muzician
author: Yingqing Xiao
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-16T00:00:00Z
review text: A holomorphic or meromorphic function which is invariant under the group of linear transformations is called an automorphic function. This paper mainly considers the dynamics of rational automorphic functions, which are called regularly ramified rational maps. There are five kinds of such groups: the cyclic group \(G_1\), the dihedral group \(G_2\), the tetrahedral group \(G_3\), the octahedral group \(G_4\) and icosahedral group \(G_5\). The dynamics of rational maps invariant under \(G_1\) and its moduli spaces has been investigated by \textit{J. Milnor} in [Exp. Math. 9, No. 4, 481--522 (2000; Zbl 0972.30013)]. This paper mainly explores the Julia sets of rational maps invariant under the other four groups. Many interesting examples are presented.
reviewed by: Tao Chen
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F45
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 37F30
zbMATH DE Number: 6919374
zbMATH Keywords: finite Kleinian group
zbMATH Keywords: ramified rational maps
zbMATH Keywords: Fatou component
zbMATH Keywords: Julia set
MaRDI profile type: Publication
full work available at URL: dcds.2018139
OpenAlex ID: W2800774290
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DOI: 10.3934/DCDS.2018139
description: scientific article; zbMATH DE number 6919374