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

Mrinal Kanti Roychowdhury, and Daniel J. Rudolph. "The Morse minimal system is finitarily Kakutani equivalent to the binary odometer." Fundamenta Mathematicae 198.2 (2008): 149-163. <http://eudml.org/doc/286590>.

@article{MrinalKantiRoychowdhury2008,
abstract = {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.},
author = {Mrinal Kanti Roychowdhury, Daniel J. Rudolph},
journal = {Fundamenta Mathematicae},
keywords = {Morse minimal system; binary odometer; finitary equivalence; Kakutani equivalence},
language = {eng},
number = {2},
pages = {149-163},
title = {The Morse minimal system is finitarily Kakutani equivalent to the binary odometer},
url = {http://eudml.org/doc/286590},
volume = {198},
year = {2008},
}

TY - JOUR
AU - Mrinal Kanti Roychowdhury
AU - Daniel J. Rudolph
TI - The Morse minimal system is finitarily Kakutani equivalent to the binary odometer
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 2
SP - 149
EP - 163
AB - 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.
LA - eng
KW - Morse minimal system; binary odometer; finitary equivalence; Kakutani equivalence
UR - http://eudml.org/doc/286590
ER -