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This article is cited in 1 scientific paper (total in 1 paper)
Alexey Borisov Memorial Volume
Degenerate Resonances and Synchronization in Nearly
Hamiltonian Systems Under Quasi-periodic Perturbations
Albert D. Morozov, Kirill E. Morozov Lobachevsky State University of Nizhny Novgorod,
pr. Gagarina 23, 603950 Nizhny Novgorod, Russia
Abstract:
Quasi-periodic nonconservative perturbations of two-dimensional nonlinear Hamil-
tonian systems are considered. The definition of a degenerate resonance is introduced and
the topology of a degenerate resonance zone is studied. Particular attention is paid to the
synchronization process during the passage of an invariant torus through the resonance zone.
The existence of so-called synchronization intervals is proved and new phenomena which have
to do with synchronization are found. The study is based on the analysis of a pendulum-type
averaged system that determines the dynamics near the degenerate resonance phase curve of
the unperturbed system.
Keywords:
nearly Hamiltonian system, degenerate resonance, quasi-periodic perturbation,
averaging, synchronization.
Received: 21.06.2022 Accepted: 22.08.2022
Citation:
Albert D. Morozov, Kirill E. Morozov, “Degenerate Resonances and Synchronization in Nearly
Hamiltonian Systems Under Quasi-periodic Perturbations”, Regul. Chaotic Dyn., 27:5 (2022), 572–585
Linking options:
https://www.mathnet.ru/eng/rcd1181 https://www.mathnet.ru/eng/rcd/v27/i5/p572
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Abstract page: | 63 | References: | 20 |
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