Abstract
Quasi-periodic nonconservative perturbations of two-dimensional nonlinear Hamiltonian 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.
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Notes
Some additional conditions are required to be fulfilled, see [5] for details.
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MSC2010
34C15, 34C27, 34C37
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Morozov, A.D., Morozov, K.E. Degenerate Resonances and Synchronization in Nearly Hamiltonian Systems Under Quasi-periodic Perturbations. Regul. Chaot. Dyn. 27, 572–585 (2022). https://doi.org/10.1134/S1560354722050057
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DOI: https://doi.org/10.1134/S1560354722050057