## Decisive Bratteli–Vershik models

### Volume 247 / 2019

Studia Mathematica 247 (2019), 251-271
MSC: Primary 37B05, 37B10; Secondary 54H20.
DOI: 10.4064/sm170519-5-2
Published online: 9 November 2018

#### Abstract

We focus on Bratteli–Vershik models of general compact zero-dimensional systems with the action of a homeomorphism. An ordered Bratteli diagram is called decisive if the corresponding Vershik map prolongs in a unique way to a homeomorphism of the whole path space of the Bratteli diagram. We prove that a compact invertible zero-dimensional system has a decisive Bratteli–Vershik model if and only if either the set of aperiodic points is dense, or its closure misses one periodic orbit.