On Connectivity of Fatou Components concerning a Family of Rational Maps

Junyang Gao and Gang Liu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 R(z, t) that A. F. Beardon proposed, we prove that R(z, t) has Fatou components with connectivities 3 and 5 for any t ∈ (0, 1/12]. Furthermore, there exists t ∈ (0, 1/12] such that R(z, t) has Fatou components with connectivity nine.

Date: 2014
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https://doi.org/10.1155/2014/621312

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:621312

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