Advisory Committee Chair
John C Mayer
Advisory Committee Members
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Laminations are models for locally connected Julia sets of complex polynomials. This paper is concerned with laminations associated with degree 3 polynomials. We introduce and discuss simplest laminations and prove that subject to certain conditions a finite collection C of periodic polygons is associated with a simplest lamination L_C. This lamination is unique with respect to some collection of pullback schemes. We apply this result to the case where the collection C consists of the orbit of a periodic chord. We then introduce and characterize simple Fatou gaps by their boundary leaves and discuss the relationship between simple Fatou gaps and identity return triangles.
Barry, Brandon Lee, "On The Simplest Lamination Of A Given Identity Return Triangle" (2015). All ETDs from UAB. 1116.