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

1991/04/12 by Shishikura, Mitsuhiro · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9201282

Abstract

It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c ∈ \bM, the Julia set of z ↦ z²+c also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.

Cited by

• Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof
• Parabolic Implosion in the Parameter Space of Cubic Polynomials

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