Two invertible dynamical systems (X, A, µ, T ) and (Y, B, ν, S) where X, Y are metrizable spaces and T, S are homeomorphisms on X and Y, are said to be ﬁnitarily orbit equivalent if there exists an invertible measure preserving mapping φ from a subset M of X of measure one to a subset of Y of full measure such that
- φ|M is continuous in the relative topology on M and _φ_−1 |φ(M) is continuous in the relative topology on φ(M),
- φ(Orb_T_(x)) = Orb_S__φ_(x) for µ-a.e. x ∈ X. In this article a ﬁnitary orbit equivalence mapping has been constructed between an irrational rotation of the circle and the binary odometer.
Cite this article
Mrinal Kanti Roychowdhury, Irrational Rotation of the Circle and the Binary Odometer are Finitarily Orbit Equivalent. Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 385–402DOI 10.2977/PRIMS/1201011787