Episturmian morphisms and a Galois theorem on continued fractions

Jacques Justin

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

  • Volume: 39, Issue: 1, page 207-215
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Justin, Jacques. "Episturmian morphisms and a Galois theorem on continued fractions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 207-215. <http://eudml.org/doc/245952>.

@article{Justin2005,
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.},
author = {Justin, Jacques},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {episturmian morphism; Arnoux-Rauzy morphism; palindrome; continued fraction; sturmian word; Episturmian morphism; Sturmian word.},
language = {eng},
number = {1},
pages = {207-215},
publisher = {EDP-Sciences},
title = {Episturmian morphisms and a Galois theorem on continued fractions},
url = {http://eudml.org/doc/245952},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Justin, Jacques
TI - Episturmian morphisms and a Galois theorem on continued fractions
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 207
EP - 215
AB - 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.
LA - eng
KW - episturmian morphism; Arnoux-Rauzy morphism; palindrome; continued fraction; sturmian word; Episturmian morphism; Sturmian word.
UR - http://eudml.org/doc/245952
ER -

References

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