Computational Methods and Function Theory 6 (2006), No. 2, 317--327
Copyright Heldermann Verlag 2006
Norbert Steinmetz
stein@math.uni-dortmund.de , Universität Dortmund, Fachbereich Mathematik, 44221 Dortmund, Germany.
In this note we prove that the so-called Sierpinski holes in the parameter plane 0<|λ|<∞ of the McMullen family Fλ(z)=zm+λ/zl, m≥ 2 and l≥1 fixed, are simply connected, and determine the total number of these domains.
Keywords: Julia set, quasiconjugation, quasiconformal mapping, Mandelbrot set, McMullen family, Sierpinski hole, Sierpinski curve.
MSC 2000: 37F10, 37F15, 37F45.
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