Morphisms fixing words associated with exchange of three intervals
Doppler Institute & Department of Mathematics, FNSPE, Czech
Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; email@example.com; firstname.lastname@example.org; email@example.com
We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.
Mathematics Subject Classification: 68R15 / 08A50
Key words: Interval exchange transformation / Sturmian morphisms / substitution invariance.
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