American Institute of Mathematical Sciences

October  2015, 35(10): 4735-4741. doi: 10.3934/dcds.2015.35.4735

Topological properties of sectional-Anosov flows

 1 Departamento de Matemática, Universidade Federal de Viçosa, Viçosa-MG, Brazil, Brazil 2 Departamento de Matemática, Universidade Federal do Rio de Janeiro, RJ, Brazil

Received  July 2014 Revised  February 2015 Published  April 2015

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.
Citation: Enoch Humberto Apaza Calla, Bulmer Mejia Garcia, Carlos Arnoldo Morales Rojas. Topological properties of sectional-Anosov flows. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 4735-4741. doi: 10.3934/dcds.2015.35.4735
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