Identifications in Escape Regions of the Parameter Space of Cubic Polynomials

Author

Chad Estabrooks, University of Rhode IslandFollow

Date of Award

2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Araceli Bonifant

Abstract

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.

Recommended Citation

Estabrooks, Chad, "Identifications in Escape Regions of the Parameter Space of Cubic Polynomials" (2018). Open Access Dissertations. Paper 734.
https://digitalcommons.uri.edu/oa_diss/734