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 affinely homeomorphic to K. Furthermore, we get that for every integer d > 1 and every Toeplitz flow (X, T), there exists a Toeplitz Z(d) - subshift which is topologically orbit equivalent to (X, T).