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It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c ∈ ∂M , the Julia set of z → 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 (1998) studied this question.
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