Three examples of three-dimensional continued fractions in the sense of Klein. (English) Zbl 1102.11007

Karpenkov, Oleg

C. R., Math., Acad. Sci. Paris 343, No. 1, 5-7 (2006).

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 \(n=3\).

Reviewer: Thomas Schmidt (Corvallis)

MSC:

11A55	Continued fractions
11J70	Continued fractions and generalizations

Keywords:

continued fractions; sails

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