Computational Methods and Function Theory

, Volume 6, Issue 2, pp 317–327

Sierpiński Curve Julia Sets of Rational Maps


DOI: 10.1007/BF03321617

Cite this article as:
Steinmetz, N. Comput. Methods Funct. Theory (2006) 6: 317. doi:10.1007/BF03321617


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

Key Words

quasiconjugation quasiconformal mapping Mandelbrot set McMullen family Sierpiński hole Sierpiński curve 

2000 MSC

37F10 37F15 37F45 

Copyright information

© Heldermann  Verlag 2006

Authors and Affiliations

  1. 1.Universität DortmundDortmundGermany

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