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.
Recommended Citation
Hill, Alexandra, "Cubic Blaschke Products" (2025). Graduate Research Theses & Dissertations. 8161.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/8161
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
