Abstract:
Bratteli diagrams have received attention in several mathematical directions,
since they were introduced by O.Bratteli for classification of C*-algebras.
In topological dynamics, Cantor minimal systems can be presented using
them, and also in a similar way they can represent ergodic probability
measure preserving transformations. Through these presentations, one can
ask what the nature of Dye's theorem on orbit equivalence becomes. The
answers are given by T.Giordano, I.Putnam, and C.Skau in the Cantor minimal
case, and by T.Hamachi and M.Keane in the finitary case, dealing with ergodic
measure preserving transformations.
Here we discuss an improvement by giving a dynamical proof of the GPS-theorem,
which was conjectured (and half of it proved) by E.Glasner and B.Weiss.
This is a joint work with Professors M.Keane (Wesleyan Univ.) and H.Yuasa
(Kyushu Univ.). |