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- Stable weakly shadowable volume-preserving systems are volume-hyperbolicPublication . Bessa, Mário; Lee, Manseob; Vaz, SandraWe 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.
- Tracing orbits on conservative mapsPublication . Bessa, MárioWe explore uniform hyperbolicity and its relation with the pseudo orbit tracing property. This property indicates that a sequence of points which is nearly an orbit (affected with a certain error) may be shadowed by a true orbit of the system. We obtain that, when a conservative map has the shadowing property and, moreover, all the conservative maps in a C1-small neighborhood display the same property, then the map is globally hyperbolic