, Volume 6, Issue 2, pp 317-327
Date: 07 Mar 2013

Sierpiński Curve Julia Sets of Rational Maps

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Abstract

In this note we prove that the so-called Sierpi\’nski holes in the parameter plane 0 < ¦λ¦ < ∞ of the McMullen family Fλ(z) = z m + λ/z , m ≥ 2 and ℓ ≥ 1 fixed, are simply connected, and determine the total number of these domains.