Title: Invariant Measures on Bratteli Diagrams
Speaker: Sergey Bezuglyi
Speaker Info: Institute for Low Temperature Physics (Kharkov, Ukraine)
The talk is devoted to the study of ergodic invariant measures on non-simple finite rank Bratteli diagrams. It is well known that the Bratteli-Vershik model is a powerful method for study aperiodic homeomorphisms of a Cantor set. In particular, this method allows one to describe completely the symplex of invariant measures for aperiodic homeomorphisms of finite rank. We first find the structure of finite rank diagrams. It is proved that every ergodic invariant measure (finite or infinite) is an extension of a finite ergodic measure defined on a simple subdiagram. We find some algebraic criteria in terms of entries of incidence matrices and their norms under which such an extension remains a finite measure. We also give an algebraic condition for a Bratteli diagram to be uniquely ergodic. It is proved that Vershik maps on finite rank Bratteli diagrams cannot be strongly mixing and always have zero entropy with respect to any finite ergodic measure.Date: Tuesday, March 30, 2010
The talk is based on joint work with J.Kwiatkowski, K.Medynets, and B.Solomyak.