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The choquet simplex of invariant measures for minimal flows

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Abstract

The set of invariant measures of a compact dynamical system is well known to be a nonempty compact metrizable Choquet simplex. It is shown that all such simplices are realized already for the class of minimal flows. Moreover, sufficient is the class of 0–1 Toeplitz flows. Previously, it is proved that the set of invariant measures of the regular Toeplitz flows contains homeomorphic copies of all metric compacta.

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  1. Institute of Mathematics, Technical University, 50-370, Wroclaw, Poland

    Tomasz Downarowicz

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  1. Tomasz Downarowicz
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Downarowicz, T. The choquet simplex of invariant measures for minimal flows. Israel J. Math. 74, 241–256 (1991). https://doi.org/10.1007/BF02775789

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  • DOI: https://doi.org/10.1007/BF02775789

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