Bessa, MárioLee, ManseobVaz, Sandra2022-11-212022-11-212014-05-15Bessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014). https://doi.org/10.1007/s10114-014-3093-8http://hdl.handle.net/10400.6/12421We prove that any C1-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 shadowinDominated splittingHyperbolicityjournal article10.1007/s10114-014-3093-8