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- W2088847488 abstract "We study (C^1)-generic vector fields on closed manifolds without points accumulated by periodic orbits of different indices. We prove that these flows exhibit finitely many sinks and sectional-hyperbolic transitive Lyapunov stable sets whose basins form a residual subset of the ambient manifold. This represents a partial positive answer to conjectures in Arbieto and Morales (Proc Am Math Soc 141:2817–2827, 2013), the Palis conjecture Palis (Nonlinearity 21:T37–T43, 2008) and gives a flow version of Crovisier and Pujals (Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms, 2010)." @default.
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- W2088847488 date "2014-07-05" @default.
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- W2088847488 title "Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows" @default.
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- W2088847488 doi "https://doi.org/10.1007/s00208-014-1061-3" @default.
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