Geodesic
On the number of invartiant measures for flows on orientable surfaces
Izvestiya. Mathematics , Tome 9 (1975) no. 4, pp. 813-830

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The following theorem is proved. For any natural numbers $n$ and $k$, $n\geqslant k$, on a two-dimensional orientable compact manifold without boundary of class $C^\infty$ and genus there exists a topologically transitive flow of class $C^\infty$ having $2n-2$ fixed points and exactly $k$ invariant ergodic normalized measures such that the measure of each trajectory is equal to zero. Bibliography: 3 items. 
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     author = {E. A. Sataev},
     title = {On the number of invartiant measures for flows on orientable surfaces},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a5/}
}
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E. A. Sataev. On the number of invartiant measures for flows on orientable surfaces. Izvestiya. Mathematics , Tome 9 (1975) no. 4, pp. 813-830. http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a5/