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arnoux-rauzy morphism

RAIRO - Theoretical Informatics and Applications (1)

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Episturmian morphisms and a Galois theorem on continued fractions
Jacques Justin
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 39 / Issue 1 / January 2005

Published online by Cambridge University Press:

15 March 2005, pp. 207-215

Print publication:

January 2005
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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.