Computational Methods and Function Theory

, Volume 6, Issue 2, pp 317–327

Sierpiński Curve Julia Sets of Rational Maps

Article

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) = 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 

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Copyright information

© Heldermann  Verlag 2006

Authors and Affiliations

  1. 1.Universität DortmundDortmundGermany

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