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Minimal models for noninvertible and not uniquely ergodic systems

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Abstract

Let (Y, S) be a (not necessarilly invertible) topological dynamical system on a zero-dimensional metric spaceY without periodic points. Then there exists a minimal system (X, T) with the same simplex of invariant measures as (Y, S). More precisely, there exists a Borel isomorphism between full sets inY andX such that the adjoint map on measures is a homeomorphism between the corresponding sets of invariant measures in the weak topology. As an application we construct a minimal system carrying isomorphic copies of all nonatomic invariant measures.

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Authors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, ul. Wybrzeze Wyspiańskiego 27, 50-370, Wrocław, Poland

    Tomasz Downarowicz

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  1. Tomasz Downarowicz
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Downarowicz, T. Minimal models for noninvertible and not uniquely ergodic systems. Isr. J. Math. 156, 93–110 (2006). https://doi.org/10.1007/BF02773826

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  • DOI: https://doi.org/10.1007/BF02773826

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