Fractions continues hermitiennes et billard hyperbolique

Pierrick Meignen

Journal de théorie des nombres de Bordeaux (1998)

  • Volume: 10, Issue: 1, page 1-15
  • ISSN: 1246-7405

Abstract

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The purpose of this paper is to describe a dynamical system ( X , T ) associated to the Hermite algorithm for the continued fraction expansion of real numbers. It is related to trajectories in hyperbolic billiards. We prove the ergodicity of T and we deduce some results.

How to cite

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Meignen, Pierrick. "Fractions continues hermitiennes et billard hyperbolique." Journal de théorie des nombres de Bordeaux 10.1 (1998): 1-15. <http://eudml.org/doc/248158>.

@article{Meignen1998,
abstract = {Nous proposons de formaliser une méthode d’approximation diophantienne dans $\mathbb \{R\}$ en considérant l’action de $PGL_2 (\mathbb \{Z\})$ sur le demi-plan complexe. On retrouvera le thème classique de la connexion entre développement en fractions continues et flots géodésiques modélisé ici par un billard hyperbolique.},
author = {Meignen, Pierrick},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Hermite continued fractions; ergodic theory; billiards; fundamental invariants},
language = {fre},
number = {1},
pages = {1-15},
publisher = {Université Bordeaux I},
title = {Fractions continues hermitiennes et billard hyperbolique},
url = {http://eudml.org/doc/248158},
volume = {10},
year = {1998},
}

TY - JOUR
AU - Meignen, Pierrick
TI - Fractions continues hermitiennes et billard hyperbolique
JO - Journal de théorie des nombres de Bordeaux
PY - 1998
PB - Université Bordeaux I
VL - 10
IS - 1
SP - 1
EP - 15
AB - Nous proposons de formaliser une méthode d’approximation diophantienne dans $\mathbb {R}$ en considérant l’action de $PGL_2 (\mathbb {Z})$ sur le demi-plan complexe. On retrouvera le thème classique de la connexion entre développement en fractions continues et flots géodésiques modélisé ici par un billard hyperbolique.
LA - fre
KW - Hermite continued fractions; ergodic theory; billiards; fundamental invariants
UR - http://eudml.org/doc/248158
ER -

References

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