Some Remarks on Palindromic Periodicities

We say a finite word x is a palindromic periodicity if there exist two palindromes p and s such that |x| ≥ |ps| and x is a prefix of the word (ps)^ω = pspsps⋯. In this paper we examine the palindromic periodicities occurring in some classical infinite words, such as Sturmian words, episturmian words, the Thue-Morse word, the period-doubling word, the Rudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a number of results about them.