Abstract:
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.
This paper was carried out within the framework of the Russian Ministry of Science and Edu-
cation [FSWR-2020-0036]. The authors acknowledge support from the Russian Science Foundation
under the grant 24-21-00050 (Sections 2–3). The numerical simulations in Section 4 were supported
by the RSF (grant 19-11-00280) (Morozov K. E.).
\Bibitem{MorMor24}
\by Kirill E. Morozov, Albert D. Morozov
\mathnet{http://mi.mathnet.ru/rcd1245}
\crossref{https://doi.org/10.1134/S1560354724010052}
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This publication is cited in the following 1 articles:
Nikita Barabash, Igor Belykh, Alexey Kazakov, Michael Malkin, Vladimir Nekorkin, Dmitry Turaev, “In Honor of Sergey Gonchenko and Vladimir Belykh”, Regul. Chaotic Dyn., 29:1 (2024), 1–5
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