Strong orbit equivalence and residuality

Abstract

We consider a class of minimal Cantor systems that up to conjugacy contains all systems strong orbit equivalent to a given system. We define a metric on this strong orbit equivalence class and prove several properties about the resulting metric space including that the space is complete and separable but not compact. 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 final result shown is that the set of systems with zero entropy is residual in every strong orbit equivalence class of this type.