Date of Award

2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Mark Comerford

Abstract

The Schlicht class of functions, commonly denoted as S, is the class of univalent functions defined on the unit disk such that f (0) = 0 and f’(0) = 1. This is a well-studied class for which many results are known. We prove that there exists a bounded sequence of polynomials, and a Fatou component for this sequence, such that for all f ∈ S, there exists a subsequence of iterates of compositions of our polynomial sequence for which f is a limit function.

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