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

Devaney, Robert

doi:10.1090/S0002-9947-2013-05948-X

A Cantor-Mandelbrot-Sierpiński tree in the parameter plane for rational maps
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Trans. Amer. Math. Soc. 366 (2014), 1095-1117 Request permission

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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