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arXiv · 1201.1464

Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows

A. Arbieto·C. A. Morales·B. Santiago
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Abstract

We study $C^1$-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 \cite{am}, the Palis conjecture \cite{pa} and extend the Araujo's thesis to higher dimensions \cite{a}.

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A. Arbieto, C. A. Morales, B. Santiago. 2012-01-06. Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows. https://arxiv.org/abs/1201.1464

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