Date of Award

2019

Degree Type

Thesis

Degree Name

Honors Thesis

Department

Mathematics

First Advisor

Scott Kaschner

Abstract

Suppose f_{n,c} is a complex-valued mapping of one complex variable given by f_{n,c}(z) = z^n + p(z) + c, where p is a polynomial such that p(0) = 0 and c is a complex parameter such that |c| < 1. We provide necessary and sufficient conditions that the geometric limit, as n approaches infinity, of the set of points that remain bounded under iteration by f_{n,c} is the disk of radius 1 centered at the origin.

Included in

Mathematics Commons

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