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DCDS

We study sectional-Anosov flows on compact $3$-manifolds.
First we prove that every periodic orbits represents an infinite order element of
the fundamental group outside the strong stable manifolds of the singularities.
Next, in the transitive case, we prove that the first Betti number of the manifold is positive, that the number of singularities is given by the Euler
characteristic and that every boundary's connected component has nonpositive Euler characteristic. Moreover, there is one component with negative
characteristic if and only if the flow has singularities. These results will be used to discuss the existence of transitive sectional-Anosov flows on
specific compact 3-manifolds with boundary.

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