Date of Project
College of Arts and Sciences
Dr. Gregory Kelsey
A finite subdivision rule is set of instructions for repeatedly subdividing a partitioning of a given space. This turns out to be incredibly useful when attempting to describe a process known as polynomial mating. Polynomial mating is a way of gluing together two spaces which two polynomials may act upon such that the glued borders of each space respects the dynamics described by each polynomial. For matings of Misiurewicz polynomials, the spaces we are gluing together are 1-dimensional and are thus all border. This poses a conceptual difficulty which this paper attempts to resolve by using finite subdivison rules to generate iterative approximations of matings between Misiurewicz polynomials with relatively simple dynamic properties.
Zonio, Jeremiah, "Finite Subdivision Rules for Matings of Quadratic Thurston maps with few postcritical points" (2022). Undergraduate Theses. 88.