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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 774–787 (Mi izv1204)  

Geodesics on the two-dimensional torus with two rotation numbers

L. V. Polterovich


Abstract: Geodesies with two arbitrary predetermined rotation numbers are constructed for Riemannian metrics on the two-dimensional torus that satisfy a special nonintegrability condition. Each of the geodesics constructed is asymptotic to two minimal geodesics with these rotation numbers and is a union of two minimal semigeodesics outside some segment of finite length.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 101–114

Bibliographic databases:

UDC: 517.91
MSC: Primary 58F17, 58F15; Secondary 57N05
Received: 07.01.1987

Citation: L. V. Polterovich, “Geodesics on the two-dimensional torus with two rotation numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 774–787; Math. USSR-Izv., 33:1 (1989), 101–114

Citation in format AMSBIB
\Bibitem{Pol88}
\by L.~V.~Polterovich
\paper Geodesics on the two-dimensional torus with two rotation numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 774--787
\mathnet{http://mi.mathnet.ru/izv1204}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966984}
\zmath{https://zbmath.org/?q=an:0675.58030}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 101--114
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000816}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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