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Episturmian morphisms and a Galois theorem on continued fractions

Published online by Cambridge University Press:  15 March 2005

Jacques Justin
Jacques Justin*
Affiliation:
Present address: 19 rue de Bagneux, 92330 Sceaux, France. LIAFA, ERS 586, Université Paris VII, case 7014, 2 place Jussieu, 75251 Paris Cedex 5, France; justin@liafa.jussieu.fr
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Abstract

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.

Keywords

Episturmian morphismArnoux-Rauzy morphismpalindromecontinued fractionSturmian word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 207 - 215
Copyright
© EDP Sciences, 2005

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