Abstract
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.
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Berstel, J., Séébold, P. (1993). A characterization of Sturmian morphisms. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_20
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DOI: https://doi.org/10.1007/3-540-57182-5_20
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