Recognizability in S-adic shifts
Résumé
We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Mossé's Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result states that a sequence of morphisms with bounded alphabet size is eventually recognizable for aperiodic points, improving and simplifying a result of Berthé et al. (2019). This also provides a new simple proof for the recognizability of a single morphism on its shift space. The main ingredient of the proof are elementary morphisms.
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