Sectional-Anosov flows in higher dimensions

TL;DR

This paper extends the understanding of sectional-Anosov flows in higher dimensions, showing that attractors near such flows necessarily contain singularities, generalizing previous three-dimensional results.

Contribution

It proves that all attractors of vector fields close to a transitive sectional-Anosov flow with singularities must contain a singularity, extending prior results to higher dimensions.

Findings

Attractors near sectional-Anosov flows have singularities.

Extension of 3D results to higher dimensions.

Reinforcement of the structure of hyperbolic attractors.

Abstract

A sectional-Anosov flow on a manifold M is a C^1 vector field inwardly transverse to the boundary for which the maximal invariant is sectional-hyperbolic. We prove that every attractor of every vector field C^1 close to a transitive sectional-Anosov flow with singularities on a compact manifold has a singularity. This extends the three-dimensional result obtained in [Morales, C.A., The explosion of singular-hyperbolic attractors].