Homeomorphisms between limbs of the Mandelbrot set-Reference-Cited by-同舟云学术

Homeomorphisms between limbs of the Mandelbrot set

Published:2011-09-23 Issue:6 Volume:140 Page:1947-1956
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Dudko Dzmitry,Schleicher Dierk

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2012-140-06/S0002-9939-2011-11047-5/S0002-9939-2011-11047-5.pdf

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