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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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/

[1] Anosov D. V., “O povedenii traektorii na ploskosti Evklida ili Lobachevskogo, nakryvayuschikh traektorii potokov na zamknutykh poverkhnostyakh, 1”, Izv. AN SSSR. Ser. matem., 51:1 (1987), 16–43 | MR | Zbl

[2] Weil A., “On systems of curves on a ring-shaped surface”, J. Indian Math. Soc., 19:5 (1931), 109–112 ; 6, 113–114 | Zbl | Zbl

[3] Pupko V. I., “O nesamoperesekayuschikhsya krivykh na zamknutykh poverkhnostyakh”, Dokl. AN SSSR, 177:2 (1967), 272–274 | MR | Zbl

[4] Anosov D. V., “O beskonechnykh krivykh na tore i zamknutykh poverkhnostyakh otritsatelnoi eilerovoi kharakteristiki”, Optimizatsiya i differentsialnye igry, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 185, 1988, 30–53 | MR

[5] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[6] Anosov D. V., Geodezicheskie potoki na zamknutykh rimanovykh mnogoobraziyakh otritsatelnoi krivizny, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 90, 1967 | MR

[7] Markley N. G., “The Poincaré–Bendixson theorem for the Klein bottle”, Trans. Amer. Math. Soc., 135 (1969), 159–165 | DOI | MR | Zbl

[8] Aranson S. Kh., “Traektorii na neorientiruemykh dvumernykh mnogoobraziyakh”, Matem. sb., 80:3 (1969), 314–333 | MR | Zbl

[9] Medvedev V. S., “O novom tipe bifurkatsii na mnogoobraziyakh”, Matem. sb., 113:3 (1980), 487–492 | MR | Zbl

[10] Aranson S. X., Grines V. Z., “O nekotorykh invariantakh dinamicheskikh sistem na dvumernykh mnogoobraziyakh (neobkhodimye i dostatochnye usloviya topologicheskoi ekvivalentnosti tranzitivnykh sistem)”, Matem. sb., 90:3 (1973), 372–402 | MR | Zbl

[11] Maier A. G., “O traektoriyakh na orientiruemykh poverkhnostyakh”, Matem. sb., 12:1 (1943), 71–84 | MR

[12] Moise E. E., Geometric topology in dimension 2 and 3, Springer, N.Y., Hdlb., Berl., 1977 | MR | Zbl