Geodesic
Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals
Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 762-779

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New results related to number theoretic model of spin chains are proved. We solve Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals. Bibliography: 24 titles.
Keywords: continued fractions, Kloosterman sums, quadratic irrationals. 
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     author = {A. V. Ustinov},
     title = {Spin chains and {Arnold's} problem on the {Gauss-Kuz'min} statistics for quadratic irrationals},
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     pages = {762--779},
     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_5_a5/}
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A. V. Ustinov. Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals. Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 762-779. http://geodesic.mathdoc.fr/item/SM_2013_204_5_a5/