The Graduate School and University Center of The City University of New York
On the Dynamics of Quasi-Self-Matings of Generalized Starlike Complex Quadratics and the Structure of the Mated Julia Sets
Abstract
dc:description.abstract<p>It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia sets of self-matings of generalized starlike quadratic polynomials, which enjoy relatively simple combinatorics. The points in the Julia sets of the mated rational maps are completely classified according to their topology. The presence and location of buried points in these Julia sets are addressed. The interconnections between complex dynamics, combinatorics, symbolic dynamics and Thurston's lamination theory are explored and utilized. The results are then extended to "quasi-self-matings".</p>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy
- Level thesis:degree_level
- Doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- The Graduate School and University Center of The City University of New York
- Year dc:date.available
- 2009
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Flek, Ross
- Advisor dc:contributor.advisor
-
- Linda Keen
- Committee members dc:contributor.committeemember
-
- Saeed Zakeri
- Jun Hu
Subjects
dc:subject × 8Identifiers
dc:identifier.*- Repository record dc:identifier
- https://academicworks.cuny.edu/gc_etds/1464
- OAI identifier oai:identifier
- oai:academicworks.cuny.edu:gc_etds-2496