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## Fundamenta Mathematicae

2008 | 198 | 2 | 149-163
Tytuł artykułu

### The Morse minimal system is finitarily Kakutani equivalent to the binary odometer

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Two invertible dynamical systems (X,𝔄,μ,T) and (Y,𝔅,ν,S), where X and Y are Polish spaces and Borel probability spaces and T, S are measure preserving homeomorphisms of X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X₀ of X of measure one onto a subset Y₀ of Y of full measure such that
(1) $ϕ|_{X₀}$ is continuous in the relative topology on X₀ and $ϕ^{-1}|_{Y₀}$ is continuous in the relative topology on Y₀,
(2) $ϕ(Orb_{T}(x)) = Orb_{S}(ϕ(x))$ for μ-a.e. x ∈ X.
(X,𝔄,μ,T) and (Y,𝔅,ν,S) are said to be finitarily evenly Kakutani equivalent if they are finitarily orbit equivalent by a mapping ϕ for which there are measurable subsets A of X and B = ϕ(A) of Y with ϕ an isomorphism of $T_{A}$ and $T_{B}$.
It is shown here that the Morse minimal system and the binary odometer are finitarily evenly Kakutani equivalent.
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Tom
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149-163
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wydano
2008
Twórcy
• Department of Mathematics, University of North Texas, Denton, TX 76203, U.S.A.
autor
• Department of Mathematics, Colorado State University, Fort Collins, CO 80523, U.S.A.
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