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

@article{Shishikura1991TheHD, title={The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets}, author={Mitsuhiro Shishikura}, journal={Annals of Mathematics}, year={1991}, volume={147}, pages={225-267} }

It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c E AM, the Julia set of z I > Z2 + C also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.

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