DCDS
Topological properties of sectional-Anosov flows
Enoch Humberto Apaza Calla Bulmer Mejia Garcia Carlos Arnoldo Morales Rojas
Discrete & Continuous Dynamical Systems - A 2015, 35(10): 4735-4741 doi: 10.3934/dcds.2015.35.4735
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.
keywords: compact manifold Sectional-Anosov flow transitive flow periodic orbit. handlebody

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