Episturmian morphisms and a Galois theorem on continued fractions

Issue		RAIRO-Theor. Inf. Appl. Volume 39, Number 1, January-March 2005 Imre Simon, the tropical computer scientist


Page(s)		207 - 215
DOI		10.1051/ita:2005012

Theoret. Informatics Appl. 39, 207-215 (2005)
DOI: 10.1051/ita:2005012

Episturmian morphisms and a Galois theorem on continued fractions

Jacques Justin^{1, 2}

¹ Present address: 19 rue de Bagneux, 92330 Sceaux, France.
² LIAFA, ERS 586, Université Paris VII, case 7014, 2 place Jussieu, 75251 Paris Cedex 5, France; justin@liafa.jussieu.fr

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.

Mathematics Subject Classification. 11A55, 68R15

Key words: Episturmian morphism -- Arnoux-Rauzy morphism -- palindrome -- continued fraction -- Sturmian word.

© EDP Sciences 2005

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