Global bifurcation of homoclinic trajectories of discrete dynamical   systems
  We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological properties of the asymptotic stable bundles. 
Jacobo Pejsachowicz, Robert Skiba
math.DS math.FA