Abstract:
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.