Branch points of substitutions and closing ordered Bratteli diagrams

We study stationary ordered Bratteli diagrams and give necessary and sufficient conditions for these orders to generate a continuous Vershik map. We apply this to finding adic representations for one sided substitution subshifts. We give an algorithm to find the branch points of a substitution, which have to be mapped to the minimal elements of such an ordering. We find adic representations for substitutions with one branch point, and also substitutions all of whose branch points are fixed.