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

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2012

Author dc:creator

• Wilkerson, Mary

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Rossi, John F.
• Kay, Leslie D.
• Haskell, Peter E.

• Combinatorial Dynamics
• Hubbard Trees
• Matings
• Finite Subdivision Rules

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05072012-142700

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/27581