The Choquet simplex of invariant measures for minimal flows (Q1182836)

It is well known that the set of invariant measures of a dynamical system on a compact space is a non-empty metrizable compact Choquet simplex \(K\). Here `Choquet' stands for the fact that for any \(x\in K\) there is a unique probability measure supported by the extremal points of \(K\) having \(x\) as its barycenter. In the present paper it is proved that for any compact metrizable Choquet simplex \(K\) there exists a minimal (i.e., every orbit is dense) dynamical system on a compact space whose set of invariant measures is affinely homeomorph to \(K\). Furthermore, this minimal dynamical system may be taken to be a dyadic Toeplitz one.