Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows

Details Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows

2012-01-06

arxiv.org/abs/1201.1464v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

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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