Institute for Mathematical Sciences

Preprint ims91-7

M. Shishikura
The Hausdorff Dimension of the Boundary of the Mandelbrot Set and Julia Sets.

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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