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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Meignen, Pierrick. Fractions continues hermitiennes et billard hyperbolique. Journal de théorie des nombres de Bordeaux, Volume 10 (1998) no. 1, pp. 1-15. http://www.numdam.org/item/JTNB_1998__10_1_1_0/

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