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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