On the conjugation of standard morphisms

AbstractLet A = a, b be an alphabet. An infinite word on A is Sturmian if it contains exactly n + 1 distinct factors of length n for every integer n. A morphism f on A is Sturmian if f(x) is Sturmian whenever x is. A morphism on A is standard if it is an element of the monoid generated by the two elementary morphisms, E which exchanges a and b, and φ the Fibonacci morphism defined by φ(a) = ab and φ(b) = a. The set of standard morphisms is a proper subset of the set of Sturmian morphisms. In the present paper, we give a characterization of Sturmian morphisms as conjugates of standard ones. We establish that Sturmian words generated by standard morphisms are characteristic words and then we prove that a morphism f generates an infinite word having the same set of factors as a characteristic word generated by a primitive standard morphism g if and only if f is a conjugate of a power of g