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Any two irreducible Markov chains are finitarily orbit equivalent

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Abstract

Two invertible dynamical systems (X, gA, 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 X 0 of X of full measure to a subset Y 0 of Y of full measure such that ϕ|x 0 is continuous in the relative topology on X 0, ϕ −1|Y 0 is continuous in the relative topology on Y 0 and ϕ(Orb T (x)) = Orb Sϕ (x) for µ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas-Pan American, 1201 West University Drive, Edinburg, TX, 78539, USA

    Mrinal Kanti Roychowdhury

  2. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Daniel J. Rudolph

Authors
  1. Mrinal Kanti Roychowdhury
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  2. Daniel J. Rudolph
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Correspondence to Daniel J. Rudolph.

Additional information

D.J. Rudolph supported in part by NSF grant DMS-0618030

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Roychowdhury, M.K., Rudolph, D.J. Any two irreducible Markov chains are finitarily orbit equivalent. Isr. J. Math. 174, 349–368 (2009). https://doi.org/10.1007/s11856-009-0117-7

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  • DOI: https://doi.org/10.1007/s11856-009-0117-7

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