Relations between Escape Regions in the Parameter Space of Cubic Polynomials

preprint2022arXivOpen access

Abstract

We describe a topological relationship between slices of the parameter space of cubic maps. In the paper \cite{CP1}, Milnor defined the curves Sn\mathcal{S}_n as the set of all cubic polynomials with a marked critical point of period pp. In this paper, we will describe a relationship between the boundaries of the connectedness loci in the curves S1\mathcal{S}_1 and S2\mathcal{S}_2.

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