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

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Roychowdhury M., Rudolph D.

Fundamenta Mathematicae

2008

tom 198

nr 2

149-163

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Roychowdhury M.

1 Rudolph D.

1 2008

Wyniki wyszukiwania

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