Geodesic
On~the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces.~II
Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 449-474

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This paper is a continuation of Part I (Izv. Akad. Nauk SSSR Ser. Mat., 1987, v. 51, № 1, p. 16–43; Math. USSR-Izv. 30 (1988), 15–38). Let $L$ be a (semi) infinite nonselfintersecting continuous curve on a closed surface of nonpositive Euler characteristic and consider the behavior at “infinity” of the curve obtained by lifting $\widetilde L$ to the universal cover: either the Lobachevsky or the Euclidean plane. The possible types of this behavior for arbitrary $\widetilde L$ turn out to be the same as those for $L$ which are semitrajectories of $C^\infty$ flows. Questions concerning the approach of to infinity along a definite direction are again considered. An example is constructed in which all points of the absolute are limit points in $\widetilde L$. Bibliography: 12 titles. 
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     author = {D. V. Anosov},
     title = {On~the behavior in the {Euclidean} or {Lobachevsky} plane of trajectories that cover trajectories of flows on closed {surfaces.~II}},
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D. V. Anosov. On~the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces.~II. Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 449-474. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a0/