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

quasiconjugationquasiconformal mappingMandelbrot setMcMullen familySierpiński holeSierpiński curve

2000 MSC


Copyright information

© Heldermann  Verlag 2006