On connectivity of Fatou components concerning a family of rational maps
type: Item
instance of: scholarly article
title: On connectivity of Fatou components concerning a family of rational maps
zbMATH Open document ID: 1474.37044
DOI: 10.1155/2014/621312
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: I. N. Baker established the existence of Fatou component with any given finite connectivity by the method of quasi-conformal surgery. M. Shishikura suggested giving an explicit rational map which has a Fatou component with finite connectivity greater than 2. In this paper, considering a family of rational maps \(R \left(z, t\right)\) that A. F. Beardon proposed, we prove that \(R \left(z, t\right)\) has Fatou components with connectivities 3 and 5 for any \(t \in \left(0, \left.1 / 12\right]\right.\). Furthermore, there exists \(t \in \left(0, \left.1 / 12\right]\right.\) such that \(R \left(z, t\right)\) has Fatou components with connectivity nine.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 7022742
Wikidata QID: Q59040044
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/621312
OpenAlex ID: W1972900710
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description: scientific article; zbMATH DE number 7022742