Groups, Geometry, and Dynamics


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Volume 8, Issue 4, 2014, pp. 1007–1045
DOI: 10.4171/GGD/255

Published online: 2014-12-31

Invariant measures and orbit equivalence for generalized Toeplitz subshifts

María Isabel Cortez[1] and Samuel Petite[2]

(1) Universidad de Santiago, Chile
(2) Université de Picardie Jules Verne, Amiens, France

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

Keywords: Toeplitz subshift, discrete group actions, invariant measures, orbit equivalence

Cortez María Isabel, Petite Samuel: Invariant measures and orbit equivalence for generalized Toeplitz subshifts. Groups Geom. Dyn. 8 (2014), 1007-1045. doi: 10.4171/GGD/255