Episturmian morphisms and a Galois theorem on continued fractions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 207-215.

We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.

DOI : 10.1051/ita:2005012
Classification : 11A55, 68R15
Mots-clés : episturmian morphism, Arnoux-Rauzy morphism, palindrome, continued fraction, sturmian word 
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     title = {Episturmian morphisms and a {Galois} theorem on continued fractions},
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Justin, Jacques. Episturmian morphisms and a Galois theorem on continued fractions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 207-215. doi : 10.1051/ita:2005012. http://archive.numdam.org/articles/10.1051/ita:2005012/

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