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2014 On Connectivity of Fatou Components concerning a Family of Rational Maps
Junyang Gao, Gang Liu
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/621312

Abstract

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 Rz,t that A. F. Beardon proposed, we prove that Rz,t has Fatou components with connectivities 3 and 5 for any t0,1/12. Furthermore, there exists t0,1/12 such that Rz,t has Fatou components with connectivity nine.

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Junyang Gao. Gang Liu. "On Connectivity of Fatou Components concerning a Family of Rational Maps." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/621312

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022742
MathSciNet: MR3191055
Digital Object Identifier: 10.1155/2014/621312

Rights: Copyright © 2014 Hindawi

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