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On Connectivity of Fatou Components concerning a Family of Rational Maps

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  • Junyang Gao
  • Gang Liu

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.

Suggested Citation

  • Junyang Gao & Gang Liu, 2014. "On Connectivity of Fatou Components concerning a Family of Rational Maps," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:621312
    DOI: 10.1155/2014/621312
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