### 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.

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.

#### Keywords

Ergodic theory; topological dynamics

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