Topology and Homoclinic Trajectories of Discrete Dynamical Systems
  We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of the linearization at the stationary branch are twisted in different ways. 
Jacobo Pejsachowicz and Robert Skiba
math.DS math.FA