  Recalling the construction of a flat surface from a Bratteli diagram, this
paper considers the dynamics of the shift map on the space of all bi-infinite
Bratteli diagrams as the renormalizing dynamics on a moduli space of flat
surfaces of finite area. A criterion of unique ergodicity similar to that of
Masur's for flat surface holds: if there is a subsequence of the renormalizing
dynamical system which has a good accumulation point, the translation flow or
Bratteli-Vershik transformation is uniquely ergodic. Related questions are
explored.
