Title page for ETD etd-05072012-142700


Type of Document Dissertation
Author Wilkerson, Mary
URN etd-05072012-142700
Title Finite Subdivision Rules from Matings of Quadratic Functions: Existence and Constructions
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Floyd, William J. Committee Chair
Haskell, Peter E. Committee Member
Kay, Leslie D. Committee Member
Rossi, John F. Committee Member
Keywords
  • Combinatorial Dynamics
  • Hubbard Trees
  • Matings
  • Finite Subdivision Rules
Date of Defense 2012-04-24
Availability unrestricted
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.
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