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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) ^ = 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.
Fici et al. (Mon,) studied this question.