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

Mathematics – Dynamical Systems

Scientific paper

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2 pages, 5 figures

Scientific paper

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
$Q\geq 3$ and $p$ is small. This gives a lower bound of the Hausdorff dimension
of the Julia sets of McMullen maps in the special cases.

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