Palindrome complexity bounds for primitive substitution sequences

We consider one-sided innnite words generated via iteration by primitive substitutions on nite alphabets and provide bounds on the palin-drome complexity function as well as uniform bounds on the frequencies of palindromes in such words. As an application of these bounds, we prove that the strongly palindromic sequences in a primitive substitution dynamical system form a set of measure zero. 1. Introduction In this paper we are concerned with a study of local reeectional symmetries in general innnite words generated by primitive substitutions. We shall study com-binatorial issues, namely, the palindrome complexity function associated to such words, as well as dynamical issues, that is, the frequencies of palindromes occurring in these words. Before we present the results we shall prove, let us recall some basic notions.