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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2024, том 29, выпуск 1, страницы 65–77 (Mi rcd1245)

Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev

Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation

Kirill E. Morozov, Albert D. Morozov

Lobachevsky State University of Nizhny Novgorod, pr. Gagarina 23, 603950 Nizhny Novgorod, Russia

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.

Ключевые слова: nearly Hamiltonian system, degenerate resonance, quasi-periodic perturbation, parametric perturbation, averaging

MSC: 34C15, 34C27, 34C37

Поступила в редакцию: 14.09.2023
Принята в печать: 14.12.2023

Язык публикации: английский

DOI: 10.1134/S1560354724010052



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