Episturmian morphisms and a Galois theorem on continued fractions
Justin, Jacques
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005), p. 207-215 / Harvested from Numdam
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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.

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/ita:2005012
Classification:  11A55,  68R15 
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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},
     volume = {39},
     year = {2005},
     pages = {207-215},
     doi = {10.1051/ita:2005012},
     mrnumber = {2132588},
     zbl = {1126.68519},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2005__39_1_207_0}
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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) pp. 207-215. doi : 10.1051/ita:2005012. http://gdmltest.u-ga.fr/item/ITA_2005__39_1_207_0/

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