Points d'orbite dense de certains langages de mots infinis (Q1093375)

By a result of Beauquier and Nivat, a doubly infinite word which is not strongly transitive is ultimately periodic in both directions, if the set of its factors is a rational language. The authors give a topological proof of that result and arrive at a slight generalization. An application to dynamic topological systems S where the set of factors is a language L(S) of the form \(X^*cY^*\) for some synchronous codes \(X,Y\subseteq \{a,b\}^*\) is indicated.