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We study the palindromic length of factors of infinite words fixed bymorphisms of the so-called class $\mathcal{P}$ introduced by Hof, Knill andSimon. We show that it grows at most logarithmically with the length of thefactor. For the Fibonacci word and the Thue-Morse word we provide estimates onthe constants of the growth. We also construct an infinite word rich inpalindromes for which the palindromic length grows as $\sqrt{n}$.

Palindromic length of words and morphisms in class $\mathcal{P}$