SHADOWING,EXPANSIVENESS AND SPECIFICATION FOR C~1-CONSERVATIVE SYSTEMS

We prove that a C~1-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,as in10,27],we prove that the C~1-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.