  An infinite word generated by a substitution is rigid if all the
substitutions which fix this word are powers of a same substitution. Sturmian
words as well as characteristic Arnoux-Rauzy words are known to be rigid. In
the present paper, we prove that all Arnoux-Rauzy words are rigid. The proof
relies on two main ingredients: firstly, the fact that the primitive
substitutions that fix an Arnoux-Rauzy word share a common power, and secondly,
the notion of normal form of an episturmian substitution (i.e., a substitution
that fixes an Arnoux-Rauzy word). The main difficulty is then of a
combinatorial nature and relies on the normalization process when taking powers
of episturmian substitutions: the normal form of a square is not necessarily
equal to the square of the normal forms.
