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 ℓ, m ≥ 2 and ℓ ≥ 1 fixed, are simply connected, and determine the total number of these domains.
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Steinmetz, N. Sierpiński Curve Julia Sets of Rational Maps. Comput. Methods Funct. Theory 6, 317–327 (2006). https://doi.org/10.1007/BF03321617
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DOI: https://doi.org/10.1007/BF03321617