On Connectivity of Fatou Components concerning a Family of Rational Maps

Junyang Gao and Gang Liu

Abstract and Applied Analysis, 2014, vol. 2014, 1-7

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

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:621312

DOI: 10.1155/2014/621312

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