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

• Autorzy: Mrinal Kanti Roychowdhury , Daniel J. Rudolph
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 2
• Strony: 149-163

Daty

wydano

2008

Twórcy

autor

Mrinal Kanti Roychowdhury

• Department of Mathematics, University of North Texas, Denton, TX 76203, U.S.A.

autor

Daniel J. Rudolph

• Department of Mathematics, Colorado State University, Fort Collins, CO 80523, U.S.A.

Identyfikatory

DOI

10.4064/fm198-2-5