Advisory Committee Chair
John C Mayer
Advisory Committee Members
Alexander Blokh
Jim Gleason
Jia Li
Sylvie Mrug
Lex Oversteegen
Document Type
Dissertation
Date of Award
2015
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
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.
Recommended Citation
Barry, Brandon Lee, "On The Simplest Lamination Of A Given Identity Return Triangle" (2015). All ETDs from UAB. 1116.
https://digitalcommons.library.uab.edu/etd-collection/1116