Berstel, Jean; Séébold, Patrice Sturmian morphisms. (Morphismes de Sturm.) (French) Zbl 0803.68095 Bull. Belg. Math. Soc. - Simon Stevin 1, No. 2, 175-189 (1994). 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. Cited in 3 ReviewsCited in 20 Documents MSC: 68R15 Combinatorics on words 20M05 Free semigroups, generators and relations, word problems 68Q45 Formal languages and automata Keywords:infinite words; iterated morphisms; Sturmian words; dynamical systems; continued fractions PDF BibTeX XML Cite \textit{J. Berstel} and \textit{P. Séébold}, Bull. Belg. Math. Soc. - Simon Stevin 1, No. 2, 175--189 (1994; Zbl 0803.68095) Full Text: EuDML OpenURL