Extremal words in morphic subshifts

International audienceGiven an infinite word x over an alphabet A, a letter b occurring in x, and a total order sigma on A, we call the smallest word with respect to sigma starting with b in the shift orbit closure of x an extremal word of x. In this paper we consider the extremal words of morphic words. If x = g(f(omega)(a)) for some morphisms f and g, we give two simple conditions on f and g that guarantee that all extremal words are morphic. This happens, in particular, when x is a primitive morphic or a binary pure morphic word. Our techniques provide characterizations of the extremal words of the period-doubling word and the Chacon word and a new proof of the form of the lexicographically least word in the shift orbit closure of the Rudin-Shapiro wor