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arXiv · 2305.07925

Symmetric cubic polynomials

A. Blokh·L. Oversteegen·N. Selinger·V. Timorin·S. Vejandla
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Abstract

We describe a model $\mathcal{M}_3^{comb}$ for the boundary of the connectedness locus $\mathcal{M}^{sy}_3$ of the parameter space of cubic symmetric polynomials $p_c(z)=z^3-3c^2z$. We show that there exists a monotone continuous function $\pi:\partial \mathcal{M}_c^{sy}\to \mathcal{M}_3^{comb}$ which is a homeomorphism if $\mathcal{M}^{sy}_3$ is locally connected.

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A. Blokh, L. Oversteegen, N. Selinger, V. Timorin, S. Vejandla. 2023-05-13. Symmetric cubic polynomials. https://arxiv.org/abs/2305.07925

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