  We study the drift of slow variables in a slow-fast Hamiltonian system with
several fast and slow degrees of freedom. For any periodic trajectory of the
fast subsystem with the frozen slow variables we define an action. For a family
of periodic orbits, the action is a scalar function of the slow variables and
can be considered as a Hamiltonian function which generates some slow dynamics.
These dynamics depend on the family of periodic orbits.
  Assuming the fast system with the frozen slow variables has a pair of
hyperbolic periodic orbits connected by two transversal heteroclinic
trajectories, we prove that for any path composed of a finite sequence of slow
trajectories generated by action Hamiltonians, there is a trajectory of the
full system whose slow component shadows the path.
