Homeomorphisms between limbs of the Mandelbrot set
Dynamical Systems
2010-09-01 v1
Abstract
We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.
Cite
@article{arxiv.1008.5355,
title = {Homeomorphisms between limbs of the Mandelbrot set},
author = {Dzmitry Dudko and Dierk Schleicher},
journal= {arXiv preprint arXiv:1008.5355},
year = {2010}
}