Hyperbolicity and Quasi-hyperbolicity in Polynomial Diffeomorphisms of   ${\Bbb C}^2$
  We consider complex Henon maps which are quasi-hyperbolic. We show that a quasi-hyperbolic map is uniformly hyperbolic if and only if there are no tangencies between stable and unstable manifolds. 
Eric Bedford, Lorenzo Guerini and John Smillie
math.DS