Bessa, MárioLee, ManseobVaz, Sandra2023-05-302023-05-302014Bessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014)http://hdl.handle.net/10400.2/13900We prove that any C^1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F . Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.engWeak shadowingDominated splittingHyperbolicityjournal article10.1007/s10114-014-3093-8