Core Entropy of Finite Subdivision Rules

The topological entropy of the subdivision map of a finite subdivision rule restricted to the 1-skeleton of its model subdivision complex, which we call textbf{core entropy}, is examined. We consider core entropy for finite subdivision rules realizing quadratic Misiurewicz polynomials and matings of such polynomials. It is shown that for a non-restrictive class of finite subdivision rules realizing quadratic Misiurewicz polynomials, core entropy equals Thurston's core entropy. We also show that the core entropy of formal and degenerate matings of Misiurewicz polynomials is determined by Thurston's core entropy of the mated polynomials.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2021

Author dc:creator

• Kim, Daniel Min

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Orr, Daniel D.
• Rossi, John F.
• Haskell, Peter E.

• finite subdivision rules
• entropy

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

vt_gsexam:30299

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/104060