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

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

2012-04-05

arxiv.org/abs/1204.1282v1

Mathematics

Dynamical Systems

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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