Title | On degenerate resonances in systems close to two-dimensional nonlinear Hamiltonian ones under quasi-periodic parametric perturbations |
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Authors | O. S. Kostromina^{1}^{1}National Research Lobachevsky State University of Nizhny Novgorod |

Annotation | Using the example of a pendulum-type equation with nonmonotonic rotation under a quasi-periodic nonconservative perturbation, the structure of the degenerate resonance zone in the case of parametric resonance is studied. Using the analysis of averaged systems, the conditions for the existence of quasi-periodic solutions are determined in the case when the order of degeneracy is greater than one. Particular attention is paid to the existence of quasi-periodic solutions of a new type, which are characteristic of parametric perturbations. Such solutions correspond to limit cycles of an averaged system that do not have generating limit cycles in the perturbed autonomous system corresponding to the original equation. |

Keywords | degenerate resonance, quasi-periodic parametric perturbations, limit cycle, pendulum-type equation, averaging. |

Citation | Kostromina O. S. ''On degenerate resonances in systems close to two-dimensional nonlinear Hamiltonian ones under quasi-periodic parametric perturbations'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 84-87. Available at: https://conf.svmo.ru/files/2024/papers/paper13.pdf. - Date of access: 12.11.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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