Palindromic sequences generated from marked morphisms

Fixed points u = φ(u) of marked and primitive morphisms φ over arbitrary alphabet are considered. We show that if u is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ has a conjugate in class P. This class was introduced by Hof, Knill and Simon (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are more general than the ones previously used by Frid (1999) or Tan (2007). As any morphism with an aperiodic fixed point over a binary alphabet is marked, our result generalizes the result of Tan. Labbé (2014) demonstrated that already over a ternary alphabet the property of morphisms to be marked is important for the validity of our theorem. The main tool used in our proof is the description of bispecial factors in fixed points of morphisms provided by Klouda (2012).