Lyapunov functions and expansive diffeomorphisms on 3D-manifolds

Let M be a three-dimensional compact connected oriented manifold and f : M → M an expansive diffeomorphism. We prove that non-wandering points have local stable or unstable sets locally separating M. This property allows us to prove that if Ω(f)=M then f is conjugate to a linear Anosov diffeomorphism and M=T^3, the three-dimensional torus.