Weak measure expansivity of C2 dynamics

Let f be a C-2-diffeomorphism with Axiom A and no cycle condition on a two-dimensional smooth manifold. In this article, we prove that if f is C-2-robustly weak measure expansive, then it is Q(2)-Anosov. Moreover, we expand the results of the C-2-diffeomorphism case into the C-2-vector field on a three-dimen-sional smooth manifold. Let X be a C-2-vector field with Axiom A and no cycle condition. We prove that if X is C-2-robustly weak measure expansive, then it is Q(2)-Anosov.