Parametric Perturbations of a Duffing–Type Equation with Nonmonotonic Rotation

Quasiperiodic parametric perturbations of a Duffing–type equation with nonmonotonic rotation are studied. It is assumed that the perturbations are nonconservative. The solutions behavior in the neighborhood of nearly degenerate resonance levels of energy is described and conditions for the existence of new resonance three–dimensional invariant tori in the extended phase space are found. Bifurcations that lead to the appearance of these solutions are also studied.