Continuum-wise expansiveness for non-conservative or conservative systems

In this paper, we show that a non-conservative vector field is robustly continuum-wise expansive if and only if it satisfies both Axiom A and the quasi-transversality condition. Moreover, a conservative vector field (divergence-free vector field, Hamiltonian system) is robustly continuum-wise expansive if and only if it is Anosov.