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

Abstract

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.

References in corpus (1)

• On the Lebesgue measure of the Julia set of a quadratic polynomial