  We consider a system of nonlocal equations driven by a perturbed periodic
potential. We construct multibump solutions that connect one integer point to
another one in a prescribed way. In particular, heteroclinc, homoclinic and
chaotic trajectories are constructed.
  This is the first attempt to consider a nonlocal version of this type of
dynamical systems in a variational setting and the first result regarding
symbolic dynamics in a fractional framework.
