We study nonconservative quasi-periodic $m$-frequency $\it parametric$ perturbations of twodimensional
nonlinear Hamiltonian systems. Our objective is to specify the conditions for the
existence of new regimes in resonance zones, which may arise due to parametric terms in the
perturbation. These regimes correspond to $(m + 1)$-frequency quasi-periodic solutions, which
are not generated from Kolmogorov tori of the unperturbed system. The conditions for the
existence of these solutions are found. The study is based on averaging theory and the analysis
of the corresponding averaged systems. We illustrate the results with an example of a Duffing
type equation.
Keywords:
resonances, quasi-periodic, parametric, averaging method, limit cycles, invariant torus, phase curves, equilibrium states
Citation:
Morozov A. D., Morozov K. E., On Quasi-Periodic Parametric Perturbations of Hamiltonian Systems, Rus. J. Nonlin. Dyn.,
2020, Vol. 16, no. 2,
pp. 369-378
DOI:10.20537/nd200210