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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homeomorphisms between limbs of the Mandelbrot set


Authors: Dzmitry Dudko and Dierk Schleicher
Journal: Proc. Amer. Math. Soc. 140 (2012), 1947-1956
MSC (2010): Primary 30D05, 37F10, 37F45; Secondary 37F25
Published electronically: September 23, 2011
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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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Additional Information

Dzmitry Dudko
Affiliation: Research I, Jacobs University, Postfach 750 561, D-28725 Bremen, Germany – and – G.-A.-Universität zu Göttingen, Bunsenstraße 3–5, D-37073 Göttingen, Germany
Email: d.dudko@jacobs-university.de

Dierk Schleicher
Affiliation: Research I, Jacobs University, Postfach 750 561, D-28725 Bremen, Germany
Email: dierk@jacobs-university.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11047-5
PII: S 0002-9939(2011)11047-5
Received by editor(s): September 7, 2010
Received by editor(s) in revised form: January 28, 2011
Published electronically: September 23, 2011
Additional Notes: The authors gratefully acknowledge support by the Deutsche Forschungsgemeinschaft to the first author in the context of the Research Training Group 1493
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.