2005/05/02 by Huaxin Lin, Lin, Huaxin
Mathematics · #4635 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA #msc:4635
paper · pdf · doi:10.48550/arxiv.math/0505028
arxiv created 2005/05/02 · arxiv updated 2009/12/01
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.