Symmetric cubic polynomials
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 $π:\partial \mathcal{M}_c^{sy}\to \mathcal{M}_3^{comb}$ which is a homeomorphism if $\mathcal{M}^{sy}_3$ is locally connected.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Advanced Topics in Algebra
Meromorphic and Entire Functions
Publication details
- Journal / source
- Arnold Mathematical Journal
- Publisher
- Association for Mathematical Research
- Volume
- 012
- Issue
- 001
- Pages
- 60–60
- Publication date
- 29 March 2026
- Language
- EN