Relations between Escape Regions in the Parameter Space of Cubic Polynomials

Abstract

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

21 pages, 12 figures