Date of Award

1-1-2010

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natual Science and Mathematics

First Advisor

Nicholas S. Ormes, Ph.D.

Second Advisor

Scott Leutenegger

Third Advisor

Alvaro Arias

Fourth Advisor

Jim Hagler

Fifth Advisor

Frederic Latrémolière

Keywords

Cantor, Dynamical systems, Entropy, Finite rank, Residual, Orbit equivalence

Abstract

In this dissertation, we consider notions of equivalence between minimal Cantor systems, in particular strong orbit equivalence. By constructing the systems, we show that there exist two nonisomorphic substitution systems that are both Kakutani equivalent and strongly orbit equivalent. We go on to define a metric on a strong orbit equivalence class of minimal Cantor systems and prove several properties about the metric space. If the strong orbit equivalence class contains a finite rank system, we show that the set of finite rank systems is residual in the metric space. The last result shown is that set of systems with zero entropy is residual in the strong orbit equivalence class of any minimal Cantor system.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Brett M. Werner

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

63 p.

Discipline

Mathematics

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