The Hausdorff Dimension of the Boundary of the Mandelbrot Set and Julia Sets 论文

摘要

It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c ∈ ∂M , the Julia set of z → z 2 + c also has Hausdorff dimension two.The proof is based on the study of the bifurcation of parabolic periodic points.