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Regular and Chaotic Dynamics, 1998, Volume 3, Issue 3, Pages 10–17
DOI: https://doi.org/10.1070/RD1998v003n03ABEH000076 (Mi rcd944) 		 
This article is cited in 28 scientific papers (total in 29 papers)

On the 70th birthday of J.Moser

Higher dimensional continued fractions

V. I. Arnold

Steklov Mathematical Institute, ul. Gublcina 8, Moscow 117966, Russia
Citations (29)
DOI: https://doi.org/10.1070/RD1998v003n03ABEH000076
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.
Received: 03.09.1998
Bibliographic databases:
Document Type: Article
MSC: 11B37, 13A99, 22A20, 41.'VG3, 52B70, C2L12
Language: English
Citation: V. I. Arnold, “Higher dimensional continued fractions”, Regul. Chaotic Dyn., 3:3 (1998), 10–17
Citation in format AMSBIB
\Bibitem{Arn98}
\by V. I. Arnold
\paper Higher dimensional continued fractions
\jour Regul. Chaotic Dyn.
\yr 1998
\vol 3
\issue 3
\pages 10--17
\mathnet{http://mi.mathnet.ru/rcd944}
\crossref{https://doi.org/10.1070/RD1998v003n03ABEH000076}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1704965}
\zmath{https://zbmath.org/?q=an:1044.11596}
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    • This publication is cited in the following 29 articles:
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