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

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

1991-04-12

arxiv.org/abs/math/9201282v1

Mathematics

Dynamical Systems

Scientific paper

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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