MORPHISMS FIXING WORDS ASSOCIATEDWITH EXCHANGE OF THREE INTERVALS

We consider words coding exchange of three intervals withpermutation (3,2,1), here called 3iet words. Recently, a characterizationof substitution invariant 3iet words was provided. We study theopposite question: what are the morphisms fixing a 3iet word? Wereveal a narrow connection of such morphisms and morphisms fixingSturmian words using the new notion of amicability