The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
Mitsuhiro Shishikura
Abstract
It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c ∈ , the Julia set of z 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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