Strong Orbit Equivalence and Residuality

<p>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.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Year dc:date.available

2010

Author dc:creator

• Werner, Brett M.

Contributors dc:contributor

• Nicholas S. Ormes, Ph.D.
• Scott Leutenegger
• Alvaro Arias
• Jim Hagler
• Frederic Latrémolière

• Cantor
• Dynamical systems
• Entropy
• Finite rank
• Residual
• Orbit equivalence
• Applied Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>

Language dc:language

en

Repository record dc:identifier

https://digitalcommons.du.edu/etd/699

OAI identifier oai:identifier

oai:digitalcommons.du.edu:etd-1698