Abstract:
We consider substitutions on countably infinite alphabet as Borel dynamical systems and build their Bratteli-Vershik models. We prove two versions of Rokhlin's lemma for such substitution dynamical systems. Using the Bratteli-Vershik model we give an explicit formula for a shift-invariant measure (finite and infinite) and provide a criterion for this measure to be ergodic (or uniquely ergodic). This is joint work with Sergii Bezuglyi and Palle Jorgensen.