  We prove that a C1-generic volume-preserving dynamical system (diffeomorphism
or flow) has the shadowing property or is expansive or has the weak
specification property if and only if it is Anosov. Finally, we prove that the
C1-robustness, within the volume-preserving context, of the expansiveness
property and the weak specification property, imply that the dynamical system
(diffeomorphism or flow) is Anosov.
