Date of Award
Doctor of Philosophy in Mathematics
We investigate a relationship between escape regions in slices of the parameter space of cubic polynomials. The focus of this work is to give a precise description of how to obtain a topological model for the boundary of an escape region in the slice consisting of all cubic polynomials with a marked critical point belonging to a two cycle. To obtain this model, we start with the unique escape region in the slice consisting of all maps with a fixed marked critical point, and make identifications which are described using the identifications which are made in the lamination of the basilica map z → z2 – 1.
Estabrooks, Chad, "Identifications in Escape Regions of the Parameter Space of Cubic Polynomials" (2018). Open Access Dissertations. Paper 734.