  The classical representation of Hamiltonian systems in terms of action-angle
variables are defined for simply connected domains such as an interior of a
homoclinic orbit. On this basis methods of (local) perturbations leading, in
particular, to chaotic systems have been studied in literature.
  We are describing a new method for constructing global action-angle variables
and successive perturbations based on a topological covering of the phase
space. The method is demonstrated for representative example of the Duffing
system.
