On the essential hyperbolicity of sectional-Anosov flows

Bautista, S.; Morales, C.

doi:10.1090/proc/12686

On the essential hyperbolicity of sectional-Anosov flows
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by S. Bautista and C. A. Morales PDF

Proc. Amer. Math. Soc. 144 (2016), 205-215 Request permission

Abstract:

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 include a characterization of essential hyperbolicity, sensitivity to the initial conditions and a relationship between the topology of $M$ and the denseness of the basin of the singularities.

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