ar X iv : m at h / 04 02 30 9 v 1 [ m at h . O A ] 1 9 Fe b 20 04 Minimal Dynamical Systems and Approximate Conjugacy ∗

نویسندگان

  • Huaxin Lin
  • Hiroki Matui
چکیده

Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product C∗-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via K-theory and C∗-algebras. For example, it is shown that two Cantor minimal systems are approximately τ -conjugate if and only if they are orbit equivalent and have the same periodic spectrum. It is also shown that two such systems are approximately K-conjugate if and only if the corresponding crossed product C∗-algebras have the same scaled ordered K-theory. Consequently, two Cantor minimal systems are approximately K-conjugate if and only if the associated transformation C∗-algebras are isomorphic. Incidentally, this approximate Kconjugacy coincides with Giordano, Putnam and Skau’s strong orbit equivalence for the Cantor minimal systems.

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تاریخ انتشار 2004