Groups, Geometry, and Dynamics
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Published online: 2014-12-31
Invariant measures and orbit equivalence for generalized Toeplitz subshiftsMaría Isabel Cortez and Samuel Petite (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