On the essential hyperbolicity of sectional-Anosov flows

الأصل · EN

We prove that every sectional-Anosov flow of a compact 3-manifold M exhibits a finite collection of hyperbolic attractors and singularities whose basins form a dense subset of M. Applications to the dynamics of sectional-Anosov flows on compact 3-manifolds include a characterization of essential hyperbolicity, sensitivity to the initial conditions (improving ams) and a relationship between the topology of the ambient manifold and the denseness of the basin of the singularities.