Identifications in Escape Regions of the Parameter Space of Cubic Polynomials

Chad Estabrooks, University of Rhode Island

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.^

Subject Area

Mathematics

Recommended Citation

Chad Estabrooks, "Identifications in Escape Regions of the Parameter Space of Cubic Polynomials" (2018). Dissertations and Master's Theses (Campus Access). Paper AAI10749457.
https://digitalcommons.uri.edu/dissertations/AAI10749457

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