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arXiv · 2606.28629

Paper Fortune Tellers in Julia sets of Generalized McMullen maps II: Sidecars and Zippers

Suzanne Boyd·Kelsey Brouwer
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Abstract

We study the family of complex rational functions known as Generalized McMullen maps, F(z) = z^n + a/z^n+b, for integer n at least 3 fixed, and complex parameters a, b with a nonzero. In prior work by the same authors, we provided a combinatorial model for a large class of maps whose Julia sets contain both infinitely many homeomorphic copies of quadratic Julia sets conjugate to the ``basilica'', and infinitely many subsets homeomorphic to a set which is obtained by starting with the basilica, then changing a finite number of pairs of external ray landing point identifications, following an algorithm we described. In this article, we generalize beyond the basilica, and provide a catalog of additional types of hyperbolic Julia sets of Generalized McMullen maps, where the ``baby'' Julia set can be any rabbit, aeroplane, or Kokopelli quadratic Julia set; that is, where the c-value can be taken from any bulb attached to the main cardioid of the Mandelbrot set, or from the main cardioid of any principal baby Mandelbrot set (no renormalizations).

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Suzanne Boyd, Kelsey Brouwer. 2026-06-26. Paper Fortune Tellers in Julia sets of Generalized McMullen maps II: Sidecars and Zippers. https://arxiv.org/abs/2606.28629

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