Strong orbit equivalence and residuality

Brett M. Werner


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.


Ergodic theory; topological dynamics

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