Le problème de l'étude les plus simple fractions continues n-dimensional en sens de Klein pour a été poser de V. Arnold. Le solution pour la case de a presenté dans les articles de E. Korkina (1995) et G. Lachaud (1995). Dans la Note présente, on étude la case de .
The problem of the investigation of the simplest n-dimensional continued fraction in the sense of Klein for was posed by V. Arnold. The answer for the case can be found in the works of E. Korkina (1995) and G. Lachaud (1995). In present Note we study the case .
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@article{CRMATH_2006__343_1_5_0, author = {Karpenkov, Oleg}, title = {Three examples of three-dimensional continued fractions in the sense of {Klein}}, journal = {Comptes Rendus. Math\'ematique}, pages = {5--7}, publisher = {Elsevier}, volume = {343}, number = {1}, year = {2006}, doi = {10.1016/j.crma.2006.04.023}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2006.04.023/} }
TY - JOUR AU - Karpenkov, Oleg TI - Three examples of three-dimensional continued fractions in the sense of Klein JO - Comptes Rendus. Mathématique PY - 2006 SP - 5 EP - 7 VL - 343 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.04.023/ DO - 10.1016/j.crma.2006.04.023 LA - en ID - CRMATH_2006__343_1_5_0 ER -
%0 Journal Article %A Karpenkov, Oleg %T Three examples of three-dimensional continued fractions in the sense of Klein %J Comptes Rendus. Mathématique %D 2006 %P 5-7 %V 343 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.04.023/ %R 10.1016/j.crma.2006.04.023 %G en %F CRMATH_2006__343_1_5_0
Karpenkov, Oleg. Three examples of three-dimensional continued fractions in the sense of Klein. Comptes Rendus. Mathématique, Tome 343 (2006) no. 1, pp. 5-7. doi : 10.1016/j.crma.2006.04.023. http://www.numdam.org/articles/10.1016/j.crma.2006.04.023/
[1] Continued Fractions, Moscow Center of Continuous Mathematical Education, Moscow, 2002
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[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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