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arXiv · 2501.07545

Paper Fortune Tellers in the combinatorial dynamics of some generalized McMullen maps with both critical orbits bounded

Suzanne Boyd·Kelsey Brouwer
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Abstract

For the family of complex rational functions known as "Generalized McMullen maps", F(z) = z^n + a/z^n+b, for complex parameters a and b, with a nonzero, and any integer n at least 3 fixed, we reveal, and provide a combinatorial model for, some new dynamical behavior. In particular, we describe a large class of maps whose Julia sets contain both infinitely many homeomorphic copies of quadratic Julia sets and infinitely many subsets homeomorphic to a set which is obtained by starting with a quadratic Julia set, then changing a finite number of pairs of external ray landing point identifications, following an algorithm we will describe.

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Suzanne Boyd, Kelsey Brouwer. 2025-01-13. Paper Fortune Tellers in the combinatorial dynamics of some generalized McMullen maps with both critical orbits bounded. https://arxiv.org/abs/2501.07545

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