Publication Date

2025

Document Type

Dissertation/Thesis

First Advisor

Fletcher, Alastair

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

Abstract

It is well known that Blaschke products can be classified as elliptic, hyperbolic, or parabolic. Based on the classification of the Blaschke product, we know that the Julia set is either the entire unit circle or a Cantor subset of the unit circle. For unicritical Blaschke products of degree d, it has been shown that the parabolic functions are parameterized by an epicycloid with d-1 cusps, with the interior of the epicycloid giving rise to the elliptic parameters, and the relative complement of the epicycloid within the unit disk providing the hyperbolic parameters. In this dissertation, we study in more detail degree three Blaschke products to divide the parameter space into elliptic, parabolic, and hyperbolic in order to discuss the corresponding Julia sets.

Extent

81 pages

Language

en

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

Included in

Mathematics Commons

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