Fractions continues hermitiennes et billard hyperbolique
Journal de Théorie des Nombres de Bordeaux, Volume 10 (1998) no. 1, pp. 1-15.

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.

Nous proposons de formaliser une méthode d’approximation diophantienne dans en considérant l’action de PGL 2 () 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.

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     title = {Fractions continues hermitiennes et billard hyperbolique},
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Pierrick Meignen. Fractions continues hermitiennes et billard hyperbolique. Journal de Théorie des Nombres de Bordeaux, Volume 10 (1998) no. 1, pp. 1-15. doi : 10.5802/jtnb.215. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.215/

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