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- Shadowing, expansiveness and specification for C1-conservative systemsPublication . Bessa, Mário; Lee, Manseob; Wen, XiaoWe prove that a C -generic volume-preserving dynamical system (diffeomor- phism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the C -robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.
- 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.