The Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps

Abstract

In this paper, we give a formula of the Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps $f_p(z)=z^Q+p/z^Q$, where $Q\ge 3$ and $p$ is small. This gives a lower bound of the Hausdorff dimension of the Julia sets of McMullen maps in the special cases.

2 pages, 5 figures

Cited by in corpus (1)

• Hyperbolic components of McMullen maps