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2013
Impact Factor

Vladimir Arnold

Gubkina st., 8, Moscow, 117966 Russia
Steklov Mathematical Institute RAS

Publications:

Arnold V. I.
Are quadratic residues random?
2010, vol. 15, no. 4-5, pp.  425-430
Abstract
Keywords: arithmetical dynamics, quadratic residue, randomness
Citation: Arnold V. I.,  Are quadratic residues random?, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 425-430
DOI:10.1134/S1560354710040027
Arnold V. I.
Higher dimensional continued fractions
1998, vol. 3, no. 3, pp.  10-17
Abstract
The higher-dimensional analogue of a continuous fraction is the polyhedral surface, bounding the convex hull of the semigroup of the integer points in a simplicial cone of the euclidian space. The article describes some conjectures and theorems, extending to such higher-dimensional continouos fraction the Lagrange theorem on quadraticirrationals and the Gauss–Kuzmin statistics.
Citation: Arnold V. I.,  Higher dimensional continued fractions, Regular and Chaotic Dynamics, 1998, vol. 3, no. 3, pp. 10-17
DOI:10.1070/RD1998v003n03ABEH000076

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