Advisory Committee Chair
John C Mayer
Advisory Committee Members
Alexander Blokh
Purushotham Bangalore
Document Type
Thesis
Date of Award
2020
Degree Name by School
Master of Science (MS) College of Arts and Sciences
Abstract
Laminations are a topological and combinatorial way to represent connected Julia sets of polynomials. A lamination is the boundary of the closed unit disk with a closed collection of chords that do not intersect on the interior of the disk. The standard d to 1 covering map of the circle represents the application of a degree d polynomial to its Julia set. The laminations of interest here are those that contain a d-gon which first returns to itself under the standard covering map by the identity (other polygons in laminations may first return rotated). It is known that a polygon that returns to itself by the identity has a maximum of d sides (Kiwi). We are particularly interested in d-gons whose sides simultaneously approach all of the criticality in the lamination. These particular d-gons seem to have a correspondence to unicritical laminations. We are exploring the correspondence between these two types of very different, yet closely related, laminations.
Recommended Citation
Hale, Cameron, "Unicritical Laminations And D-Gons Of Single Critical Moment" (2020). All ETDs from UAB. 673.
https://digitalcommons.library.uab.edu/etd-collection/673