Room P3.31, Mathematics Building

Tomasz Downarowicz, Wroclaw University of Technology
Minimal realizations of Jewett-Krieger type for nonuniquely ergodic systems II

In a topological dynamical system (X,T) the set of invariant measures is a Choquet simplex K(X,T) whose extreme points are ergodic measures. We will prove that for any zero-dimensional system (X,T) having no periodic points there exists a minimal system (Y,S) and an affine homeomorphism f between the Choquet simplexes K(X,T) and K(Y,S) such that for each m in K(X,T) the measure-theoretic systems (X,m,T) and (Y,f(m),S) are isomorphic. In this sense (Y,S) is a minimal model for (X,T). As an application we will derive the existence of minimal models with a preset collection of invariant measures (arranged in form of a simplex).