A Cantor-Mandelbrot-Sierpiński tree in the parameter plane for rational maps
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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.References
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Additional Information
- Robert L. Devaney
- Affiliation: Department of Mathematics, Boston University, 111 Cummington Mall, Boston, Massachusetts 02215
- MR Author ID: 57240
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 1095-1117
- MSC (2010): Primary 37F10; Secondary 37F45
- DOI: https://doi.org/10.1090/S0002-9947-2013-05948-X
- MathSciNet review: 3130327