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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.

MSC:

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