Invariant measures and orbit equivalence for generalized Toeplitz subshifts

Abstract

We show that for every metrizable Choquet simplex $K$ and for every group $G$, which is infinite, countable, amenable and residually finite, there exists a Toeplitz $G$-subshift whose set of shift-invariant probability measures is affine homeomorphic to $K$. Furthermore, we get that for every integer $d\ge 1$ and every Toeplitz flow $(X,T)$, there exists a Toeplitz ${\mathbb{Z}}^d$-subshift which is topologically orbit equivalent to $(X,T)$.

This is a new version of the old paper "Set of invariant measures of generalized Toeplitz subshifts". In this version the results are more general

References in corpus (1)

• $G$-odometers and their almost 1-1 extensions