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 combinatorial and topological model for studying the Julia sets of complex polynomials. Every complex polynomial of degree d has d fixed points counted with multiplicity. From the point of view of laminations, exactly d−1 of these fixed points are peripheral (approachable from outside the Julia set of the polynomial). Hence, at least one of the d fixed points is “hidden” from the laminational point of view. The purpose of this thesis is to identify, classify and count the possible fixed point portraits for any lamination of degree d. We will identify the “simplest” lamination for a given fixed point portrait and will show that there are polynomials that have these simplest laminations. We extend σd to D as a branched covering map. In future work with others, we want to apply Thurston’s criterion to show there exists a complex polynomial whose lamination this is.
Aziz, Md. Abdul, "Canonical Laminations for Fixed Point Portraits" (2023). All ETDs from UAB. 93.