Finite Subdivision Rules from Matings of Quadratic Functions: Existence and Constructions

TR Number

Date

2012-04-24

Journal Title

Journal ISSN

Volume Title

Publisher

Virginia Tech

Abstract

Combinatorial methods are utilized to examine preimage iterations of topologically glued polynomials. In particular, this paper addresses using finite subdivision rules and Hubbard trees as tools to model the dynamic behavior of mated quadratic functions. Several methods of construction of invariant structures on modified degenerate matings are detailed, and examples of parameter-based families of matings for which these methods succeed (and fail) are given.

Description

Keywords

Combinatorial Dynamics, Hubbard Trees, Matings, Finite Subdivision Rules

Citation