Geodesic
Limit sets at infinity for liftings of non-self-intersecting curves on the torus to the plane
Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 667-679

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In this paper Anosov's initial description of the sets mentioned in the title is completed. It is proved that there are four types of such sets and that all of these types are realizable. 
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     author = {A. A. Glutsyuk},
     title = {Limit sets at infinity for liftings of non-self-intersecting curves on the torus to the plane},
     journal = {Matemati\v{c}eskie zametki},
     pages = {667--679},
     publisher = {mathdoc},
     volume = {64},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a3/}
}
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A. A. Glutsyuk. Limit sets at infinity for liftings of non-self-intersecting curves on the torus to the plane. Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 667-679. http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a3/