Conjugation of standard morphisms and a generalization of singular words

We study the action of right conjugates of a standard morphism on the infinite word (if it exists) generated by this morphism. When g is the i-th right conjugate of a standard morphism generating an infinite word {\bf x}, g({\bf x}) is the i-th conjugate of {\bf x}. We design an algorithm to obtain a canonical decomposition of all the right conjugates of a standard morphism. As an application we compute the sequence of conjugates of the powers of the Fibonacci morphism and then we generalize, to all the conjugates of {\bf F}, Wen and Wen's decomposition of the Fibonacci word {\bf F} in singular words.