Episturmian words and episturmian morphisms

摘要

Infinite episturmian words are a generalization of Sturmian words which includes the AmouxRauzy sequences. We continue their study and that of episturmian morphisms, begun previously, in relation with the action of the shift operator. Palindromic and periodic factors of these words are described. We consider, in particular, the case where these words are generated by morphisms and introduce then a notion of intercept generalizing that of Sturmian words. Finally, we prove that the frequencies of the factors in a strong sense do exist for all episturmian words.