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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Cantor-Mandelbrot-Sierpiński tree in the parameter plane for rational maps


Author: Robert L. Devaney
Journal: Trans. Amer. Math. Soc. 366 (2014), 1095-1117
MSC (2010): Primary 37F10; Secondary 37F45
Published electronically: August 8, 2013
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Abstract: In this paper we prove the existence of a Cantor-Mandelbrot-Sierpiński tree (a CMS tree) in the parameter plane for the family of rational maps $ z^2 + \lambda /z^2$. This tree consists of a main trunk that is a Cantor necklace. Infinitely many Cantor necklaces branch off on either side of the main trunk, and between each of these branches is a copy of a Mandelbrot set.


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Additional Information

Robert L. Devaney
Affiliation: Department of Mathematics, Boston University, 111 Cummington Mall, Boston, Massachusetts 02215

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05948-X
PII: S 0002-9947(2013)05948-X
Received by editor(s): November 5, 2011
Received by editor(s) in revised form: August 17, 2012
Published electronically: August 8, 2013
Additional Notes: This work was partially supported by grant #208780 from the Simons Foundation
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.