Sturmian morphisms. (Morphismes de Sturm.) (French) Zbl 0803.68095

Summary: A morphism is called Sturmian if it preserves all Sturmian (infinite) words. It is weakly Sturmian if it preserves at least one Sturmian word. We prove that a morphism is Sturmian if and only if it keeps the word \(ba^ 2 ba^ 2 baba^ 2 bab\) balanced. As a consequence, weakly Sturmian morphisms are Sturmian. An application to infinite words associated to irrational numbers is given.


68R15 Combinatorics on words
20M05 Free semigroups, generators and relations, word problems
68Q45 Formal languages and automata
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