Homeomorphisms between limbs of the Mandelbrot set

Details Homeomorphisms between limbs of the Mandelbrot set Homeomorphisms between limbs of the Mandelbrot set

2010-08-31

arxiv.org/abs/1008.5355v1

Mathematics

Dynamical Systems

Scientific paper

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.

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