Aperiodic substitution systems and their Bratteli diagrams

We study aperiodic substitution dynamical systems arising from non-primitive substitutions. We prove that the Vershik horneornorphism phi of it stationary ordered Bratteli diagram is topologically conjugate to an aperiodic substitution system if and only if no restriction of phi to a minimal component is conjugate to an odometer. We also show that every aperiodic substitution system generated by a substitution with nesting property is conjugate to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitution system is recognizable. The classes of m-primitive substitutions and derivative substitutions associated with them are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.