ar X iv : 0 90 7 . 28 76 v 1 [ m at h . D S ] 1 6 Ju l 2 00 9 Bratteli - Vershik representations of some one - sided substitution subshifts †

We study one-sided substitution subshifts, and how they can be respresented using Bratteli-Vershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element, and we call these substitutions quasi-invertible. We characterise these substitutions, and show that if the substitution is left proper, then the subshift is equal to another substitution subshift where the non-shift invertible point is the substitution fixed point. We use these results to prove that any quasi-invertible substitution subshift has either a Bratteli-Vershik representation, or a ‘pinched’ such representation.