Geodesic
Geodesics on the two-dimensional torus with two rotation numbers
Izvestiya. Mathematics , Tome 33 (1989) no. 1, pp. 101-114.

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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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L. V. Polterovich. Geodesics on the two-dimensional torus with two rotation numbers. Izvestiya. Mathematics , Tome 33 (1989) no. 1, pp. 101-114. http://geodesic.mathdoc.fr/item/IM2_1989_33_1_a4/

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