Hubbard trees and their properties.

A Hubbard tree is a set of points at the core of dendritic Julia sets. These trees encapsulate all the information about the larger Julia set, but in a much smaller, easier to understand structure. We discuss the structure of Hubbard trees, in particular, we provide a useful definition of branch point and endpoint. Afterwards, we demonstrate the existence of some trees that cannot be Hubbard trees in any meaningful context. Later, we turn our attention to the structure of inverse limits of Hubbard trees, making use of the definition of branch point and endpoint tenured earlier in the work and demonstrate that one Hubbard tree, with minor alterations, can generate infinitely many mutually non-homeomorphic inverse limits.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2023

Author dc:creator

• Hammon, Cordell, 1996-

Advisor dc:contributor.advisor

• Meddaugh, Jonathan.

• Julia sets.
• Hubbard trees.
• Dynamical systems.
• Endpoint.
• Branch points.
• Inverse limits.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/12467

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/12467