Conjugates of characteristic Sturmian words generated by morphisms

This article is concerned with characteristic Sturmian words of slope α and 1 - α (denoted by c α and c 1-α resp.), where α ∈ (0,1) is an irrational number such that α=[0; 1 + d 1 , d 2 ,...,d n ] with d n ≥ d 1 ≥ 1. It is known that both c α and c 1-α are fixed points of non-trivial (standard) morphisms σ and σ α and c 1-α are generated by the respective morphisms σ and σ α (and hence c 1-α ) into generalized adjoining singular words, by considering conjugates of powers of the standard morphism σ by which it is generated. This extends a recent result of Leve and Seebold on conjugates of the infinite Fibonacci word.