Fractions continues hermitiennes et billard hyperbolique
Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 1, pp. 1-15.

Nous proposons de formaliser une méthode d’approximation diophantienne dans ℝ en considérant l’action de PGL2(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.

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.

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

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