Geodesic
Trajectories on nonorientable two-dimensional manifolds
Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 297-313

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This paper studies the question of decomposition of a closed nonorientable two-dimensional manifold of arbitrary genus into maximal connected components (cells), consisting of trajectories which behave “similarly” in the sense of stability of orbits and in the sense of geometrical equivalence. Figures: 2. Bibliography: 20 titles. 
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     author = {S. Kh. Aranson},
     title = {Trajectories on nonorientable two-dimensional manifolds},
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S. Kh. Aranson. Trajectories on nonorientable two-dimensional manifolds. Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 297-313. http://geodesic.mathdoc.fr/item/SM_1969_9_3_a1/