no. 1
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
Keywords: episturmian morphism, Arnoux-Rauzy morphism, palindrome, continued fraction, sturmian word 
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     author = {Justin, Jacques},
     title = {Episturmian morphisms and a {Galois} theorem on continued fractions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {207--215},
     year = {2005},
     publisher = {EDP Sciences},
     volume = {39},
     number = {1},
     doi = {10.1051/ita:2005012},
     mrnumber = {2132588},
     zbl = {1126.68519},
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     url = {https://www.numdam.org/articles/10.1051/ita:2005012/}
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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

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