Date of Award
Nicholas S. Ormes
Cantor, Dynamical Systems, Entropy, Finite Rank, Residual, (Strong) Orbit Equivalence
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.
Werner, Brett M., "Strong Orbit Equivalence and Residuality" (2010). Electronic Theses and Dissertations. 699.
Recieved from ProQuest
Brett M. Werner