Advisory Committee Chair
John C Mayer
Advisory Committee Members
Date of Award
Degree Name by School
Master of Science (MS) College of Arts and Sciences
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.
Hale, Cameron, "Unicritical Laminations And D-Gons Of Single Critical Moment" (2020). All ETDs from UAB. 673.