On the Dynamics of Quasi-Self-Matings of Generalized Starlike Complex Quadratics and the Structure of the Mated Julia Sets

Author

Ross Flek, The Graduate Center, City University of New YorkFollow

Date of Degree

2009

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Linda Keen

Committee Members

Saeed Zakeri

Jun Hu

Subject Categories

Mathematics

Keywords

Pure sciences, Complex dynamics, Complex quadratics, Fatou chains, Julia sets, Laminations, Matings

Abstract

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".

Comments

Digital reproduction from the UMI microform.

Recommended Citation

Flek, Ross, "On the Dynamics of Quasi-Self-Matings of Generalized Starlike Complex Quadratics and the Structure of the Mated Julia Sets" (2009). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1464