The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
classification
🧮 math.DS
keywords
dimensionhausdorffboundaryjuliamandelbrotbifurcationgenericmapsto
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It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \in \bM$, 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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