Baby Mandelbrot centers in the generalized McMullen subfamily

For each n3n\geq 3, consider the family rn,ar_{n,a} in the aa-plane and the parameters aka_k associated with the potential centers of hyperbolic components, where kk is odd and k=1,2,,2n1k=1,2,\ldots,2n-1. Baby Mandelbrot center conjecture. The n2n-2 parameters aka_k with odd indices k=3,,2n3k=3,\ldots,2n-3 are each centers of a baby Mandelbrot set in the aa-plane for the family rn,ar_{n,a}; the parameters a1a_1 and a2n1a_{2n-1} are excluded. The claim is presented as a suggestion based on the preceding dynamical analysis, and no proof or resolution is supplied.

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Primary source

Suzanne Boyd, Kelsey Brouwer and Matthew Hoeppner, “Exploring baby Julia sets in parameter space slices for Generalized McMullen Maps”, arXiv:2512.06992 (2026).

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