Аннотация:
We study nonconservative quasi-periodic (with $m$ frequencies) perturbations of
two-dimensional Hamiltonian systems with nonmonotonic rotation. It is assumed that the
perturbation contains the so-called parametric terms. The behavior of solutions in the vicinity
of degenerate resonances is described. Conditions for the existence of resonance $(m + 1)$-
dimensional invariant tori for which there are no generating ones in the unperturbed system
are found. The class of perturbations for which such tori can exist is indicated. The results are
applied to the asymmetric Duffing equation under a parametric quasi-periodic perturbation.