Prolongements homographiques de substitutions de mots de Christoffel. (Homographic prolongations of substitutions of Christoffel’s words). (French) Zbl 0768.11024

This paper follows a previous one by the author and J.-P. Borel [C. R. Acad. Sci., Paris, Sér. I 313, 483-485 (1991; Zbl 0742.11013)], and is devoted to the Christoffel words. It contains a generalization of a result of T. Brown which gives a characterization of the quadratic numbers as the slopes of certain infinite Christoffel words fixed under substitutions.
Note a repeated misprint: in French there should be no s at the end of the word standard in an expression like “substitutions standard”.


11J99 Diophantine approximation, transcendental number theory
11B85 Automata sequences
68R15 Combinatorics on words
68Q45 Formal languages and automata


Zbl 0742.11013