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Three examples of three-dimensional continued fractions in the sense of Klein. (English) Zbl 1102.11007
Author’s abstract: The problem of the investigation of the simplest $$n$$-dimensional continued fraction in the sense of Klein for $$n\geq 2$$ was posed by V. Arnold. The answer for the case in which $$n=2$$ can be found in the works of E. I. Korkina [Tr. Mat. Inst. Steklova 209, 143–166 (1995; Zbl 0883.11034)] and G. Lachaud [“Voiles et polyèdres de Klein”, Preprint 95–22, Lab. Math. Discrètes, CNRS, Marseille (1995)]. In this paper we study the case in which $$n=3$$.

##### MSC:
 11A55 Continued fractions 11J70 Continued fractions and generalizations
##### Keywords:
continued fractions; sails
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##### References:
 [1] Arnold, V.I., Continued fractions, (2002), Moscow Center of Continuous Mathematical Education Moscow · Zbl 1044.11596 [2] Karpenkov, O.N., On tori decompositions associated with two-dimensional continued fractions of cubic irrationalities, Funct. anal. appl., 38, 2, 28-37, (2004) · Zbl 1125.11042 [3] Korkina, E.I., Two-dimensional continued fractions. the simplest examples, Proc. Steklov inst. math., 209, 143-166, (1995) · Zbl 0883.11034 [4] G. Lachaud, Voiles et Polyèdres de Klein, preprint no. 95-22, Laboratoire de Mathématiques Discrètes du C.N.R.S., Luminy, 1995 [5] J.-O. Moussafir, Voiles et Polyédres de Klein: Geometrie, Algorithmes et Statistiques, docteur en sciences thése, Université Paris IX-Dauphine, 2000
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