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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
Posted:
September 23, 2011
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References |
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Additional Information
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
Posted:
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 after
28 years from publication.
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