Submitted by math_admin on Fri, 02/21/2020 - 17:13
preprint-id:
preprint-title:
The Hausdorff Dimension of the Boundary of the Mandelbrot Set and Julia Sets
preprint-abstract:
It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \in \partial M$, 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.
preprint-year:
1991