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The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets

Mitsuhiro Shishikura
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Abstract

It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \in \bM$, the Julia set of $z \mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.

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Mitsuhiro Shishikura. 1991-04-12. The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets. https://arxiv.org/abs/math/9201282

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