Baby Mandelbrot centers in the generalized McMullen subfamily

About 1 year old · traced to

For each n≥3n\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,…,2n−1k=1,2,\ldots,2n-1. Baby Mandelbrot center conjecture. The n−2n-2 parameters aka_k with odd indices k=3,…,2n−3k=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 a2n−1a_{2n-1} are excluded. The claim is presented as a suggestion based on the preceding dynamical analysis, and no proof or resolution is supplied.

References

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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.