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

Mrinal Kanti Roychowdhury ; Daniel J. Rudolph

Fundamenta Mathematicae, Tome 201 (2008), p. 149-163 / Harvested from The Polish Digital Mathematics Library

Résumé

Two invertible dynamical systems (X,,μ,T) and (Y,,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,,μ,T) and (Y,,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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Publié le : 2008-01-01

Zbl 1137.28003

EUDML-ID : urn:eudml:doc:286590