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

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\u27s lamination theory are explored and utilized. The results are then extended to quasi-self-matings

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

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\u27s lamination theory are explored and utilized. The results are then extended to quasi-self-matings