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.

中文翻译：

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非单调旋转二维哈密顿系统的准周期参数扰动

我们研究具有非单调旋转的二维哈密顿系统的非保守准周期（具有\(m\)频率）扰动。假设扰动包含所谓的参数项。描述了简并共振附近溶液的行为。找到了共振\((m+1)\)维不变环面存在的条件，且在未扰动系统中不存在生成环面。指出了这种环面可能存在的扰动类别。将结果应用于参数准周期摄动下的非对称 Duffing 方程。