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Session 16. Ergodic Theory and Dynamical Systems
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Minimal models for actions of amenable groups |
Bartosz Frej, Wroc law University of Technology, Poland
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The talk is based on the joint work with Dawid Huczek
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We prove that on a metrizable, compact, zero-dimensional space
every free action of an amenable group is measurably isomorphic to a
minimal \(G\)-action with the same, i.e. affinely homeomorphic,
simplex of measures. This is a continuation of earlier results by
Tomasz Downarowicz [1] and Agata Kwaśnicka and the
speaker [2]. The main motivation for this kind of study is
the famous Jewett-Krieger theorem: to any ergodic and invertible
measure-preserving map there exists an isomorphic strictly ergodic
(i.e. uniquely ergodic and minimal) homeomorphism.
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References- T.Downarowicz, Minimal models for
noninvertible and not uniquely ergodic systems , Israel Journal
Math. 156, 2006, 93-110.
- B.Frej and A.Kwaśnicka Minimal models for
\(\mathbb{Z}^d\)-actions, Colloq. Math. 110, 2008,
No. 2, 461-476.
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