Finite-rank Bratteli-Vershik diagrams are expansive -- a new proof

Abstract

In the paper "Finite-rank Bratteli-Vershik diagrams are expansive" [DM], Downarowicz and Maass proved that the Cantor minimal system associated to a properly ordered Bratteli diagram of finite rank is either an odometer system or an expansive system. We give a new proof of this truly remarkable result which we think is more transparent and easier to understand. We also address the question (QUESTION 1) raised in [DM] and we find a better (i.e. lower) bound than the one given in [DM]. In fact, we conjecture that the bound we have found is optimal.