Center manifolds for partially hyperbolic set without strong unstable   connections
  We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set K is contained in a locally invariant center submanifold if and only if each strong stable and strong unstable leaf intersects K at exactly one point. 
Christian Bonatti and Sylvain Crovisier
math.DS