On the generalization of the study of a letter power substitution on modulo-recurrent words

Let us consider an infinite word and k≥ 1 an integer. By steps of k, we substitute a letter ofthis infinite word by the power of an external letter. The new word obtaining by this process is called k to k substitution of a power letter. After the application of this new notion on modulo-reccurent words and in particular on Sturmian words. We establish the complexity function of those words.