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arXiv · 1008.5355

Homeomorphisms between limbs of the Mandelbrot set

Dzmitry Dudko·Dierk Schleicher
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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.

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Dzmitry Dudko, Dierk Schleicher. 2010-08-31. Homeomorphisms between limbs of the Mandelbrot set. https://arxiv.org/abs/1008.5355

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