EPISTURMIAN MORPHISMS AND A GALOIS THEOREM ON CONTINUED FRACTIONS

摘要

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.