Quasiperiodic Perturbations of Twodimensional Hamiltonian Systems with Nonmonotone Rotation

We study quasiperiodic nonconservative perturbations of two-dimensional Hamiltonian systems with nonmonotone rotation. We study the behavior of solutions in neighborhoods of resonance energy levels close to degenerate ones. We find conditions for the existence of resonance quasiperiodic solutions (m-dimensional invariant tori in the extended phase space) and study bifurcations in resonance zones. The results are illustrated by an example of asymmetric Duffing equation for which we also solve the problem of constructing solutions of unperturbed equations.