On Connectivity of Fatou Components concerning a Family of Rational Maps

الملخص EN

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 t∈0,1/12.

Furthermore, there exists t∈0,1/12 such that Rz,t has Fatou components with connectivity nine.