On the number of invartiant measures for flows on orientable surfaces

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.
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