Geodesic
On the structure of quasiminimal sets of foliations on surfaces
Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 397-424

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Foliations on compact surfaces are considered in this paper. The structure of a quasiminimal set is studied, and criteria for the recurrence of a nonclosed leaf are proved. The concept of an amply situated quasiminimal set is introduced, and the nonexistence of such sets on some orientable and nonorientable surfaces is proved. A sharp estimate of the number of quasiminimal sets of foliations on compact surfaces is given. These results are applied to an estimate of the number of one-dimensional basic sets of $A$-diffeomorphisms of surfaces. 
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     title = {On the structure of quasiminimal sets of foliations on surfaces},
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S. Kh. Aranson; E. V. Zhuzhoma. On the structure of quasiminimal sets of foliations on surfaces. Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 397-424. http://geodesic.mathdoc.fr/item/SM_1995_82_2_a9/