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Homeomorphisms between limbs of the Mandelbrot set

Published 2010-08-31Version 1

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.

Categories: math.DS

Keywords: mandelbrot set, hyperbolic component, homeomorphism preserves periods, equal denominators

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