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