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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Werner, Brett M."],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Nicholas S. Ormes, Ph.D.","Scott Leutenegger","Alvaro Arias","Jim Hagler","Frederic Latrémolière"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T02:03:03Z","subjects":["Cantor","Dynamical systems","Entropy","Finite rank","Residual","Orbit equivalence","Applied Mathematics","Physical Sciences and Mathematics"],"languages":["en"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
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"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Strong Orbit Equivalence and Residuality"]}]}],"canonical_facts":{"dc:contributor":["Nicholas S. Ormes, Ph.D.","Scott Leutenegger","Alvaro Arias","Jim Hagler","Frederic Latrémolière"],"dc:creator":["Werner, Brett M."],"dc:date.available":["2001-01-01T08:00:00Z"],"dc:description.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.
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"],"dc:subject":["Cantor","Dynamical systems","Entropy","Finite rank","Residual","Orbit equivalence","Applied Mathematics","Physical Sciences and Mathematics"],"dc:title":["Strong Orbit Equivalence and Residuality"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:03:03Z"}