Geodesic
On a multidimensional generalization of Lagrange's theorem on continued fractions
Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 47-61

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We prove a multidimensional analogue of the classical Lagrange theorem on continued fractions using Klein polyhedra as a multidimensional generalization of continued fractions. 
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     author = {O. N. German and E. L. Lakshtanov},
     title = {On a multidimensional generalization of {Lagrange's} theorem on continued fractions},
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O. N. German; E. L. Lakshtanov. On a multidimensional generalization of Lagrange's theorem on continued fractions. Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/IM2_2008_72_1_a2/