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Episturmian morphisms and a Galois theorem on continued fractions. (English) Zbl 1126.68519

Summary: 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.

MSC:

68R15 Combinatorics on words
11A55 Continued fractions
37B10 Symbolic dynamics
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