Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows
Abstract
We study C1-generic vector fields on closed manifolds without points accumulated by periodic orbits of different indices and prove that they exhibit finitely many sinks and sectional-hyperbolic transitive Lyapunov stable sets with residual basin of attraction. This represents a partial positive answer to conjectures in am, the Palis conjecture pa and extend the Araujo's thesis to higher dimensions a.
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