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

Abstract

Downarowicz and Maass (Ergod. Th. and Dynam. Sys. 28 (2008), 739–747) 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 by Downarowicz and Maass and we find a better (i.e. lower) bound. In fact, we conjecture that the bound we have found is optimal.