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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- April 1991
- DOI:
- 10.48550/arXiv.math/9201282
- arXiv:
- arXiv:math/9201282
- Bibcode:
- 1992math......1282S
- Keywords:
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- Mathematics - Dynamical Systems