On a Smale Conjecture for the existence of fixed points for Anosov   diffeomorphisms
  We prove that if the stable foliation and the unstable foliation of an Anosov diffeomorphism on a connected compact manifold are $C^3$, then the diffeomorphism has fixed points. This is a partial positive answer to a Smale conjecture for fixed points of Anosov diffeomorphisms. 
Tomoo Yokoyama
math.DS