Shadowing, expansiveness and specification for C¹-conservative systems

We prove that a C¹-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 C¹-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.