Some Algebraic Aspects of Dynamics on Cantor Set **
Maryam Hosseini (IPM, Teerã, Irã)
**By the Jewett-Krieger theorems every ergodic system on a Lebesgue space is isomorphic to (or realized by) a minimal ergodic system on Cantor set. So classifying Cantor minimal systems plays central role for such realizations. Classiﬁcation of Cantor minimal systems up to Orbit Equivalence has interested some mathematicians in the recent decades and was successfully done for uniquely ergodic systems by Giordano-Putnam-Skau in 1995. The main useful object in these studies is Dimension Group which has made connections between Cantor minimal systems and operator algebra. In this talk after reviewing some basic stuﬀ, I try to show that how this algebraic tools help us to know about spectral properties of Cantor minimal systems and so to a better understanding of mixing properties of these systems. This presentation is based on two recent joint works with Theirry Giordano and David Handelman in Ottawa and Fabien Durand and Samuel Petite in Amiens