ar X iv : m at h / 05 05 02 8 v 1 [ m at h . O A ] 2 M ay 2 00 5 Furstenberg Transformations and Approximate Conjugacy ∗

نویسنده

  • Huaxin Lin
چکیده

Let α and β be two Furstenberg transformations on 2-torus associated with irrational numbers θ1, θ2, integers d1, d2 and Lipschitz functions f1 and f2. We show that α and β are approximately conjugate in a measure theoretical sense if (and only if) θ1 ± θ2 = 0 in R/Z. Closely related to the classification of simple amenable C∗-algebras, we show that α and β are approximately K-conjugate if (and only if) θ1 ± θ2 = 0 in R/Z and |d1| = |d2|. This is also shown to be equivalent to that the associated crossed product C∗-algebras are isomorphic.

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تاریخ انتشار 2005