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Episturmian morphisms and a Galois theorem on continued fractions

By Jacques Justin

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

Topics: Episturmian morphism, Arnoux-Rauzy morphism, palindrome, continued fraction, Sturmian word.
Publisher: EDP Sciences
Year: 2005
DOI identifier: 10.1051/ita:2005012/pdf
OAI identifier: oai:edpsciences.org:dkey/10.1051/ita:2005012
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