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On the conditions for the existence of degenerate resonance levels in pendulum equations under quasiperiodic nonconservative parametric perturbations
| Title | On the conditions for the existence of degenerate resonance levels in pendulum equations under quasiperiodic nonconservative parametric perturbations |
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| Authors | O. S. Kostromina1 1National Research Lobachevsky State University of Nizhny Novgorod |
| Annotation | An analytical and numerical study of the period of motion on closed phase curves for pendulum equations with nonlinearity in the form of a trigonometric polynomial of the second and third degree is carried out. Conditions for the existence of degenerate levels with degeneracy orders $j=2$ and $j=3$ for such equations are determined. Under the action of quasiperiodic nonconservative perturbations, a degenerate level can become a resonance level (under the condition of commensurability of the natural frequency of the corresponding unperturbed system with the frequencies of the quasiperiodic perturbation). Then we say that a degenerate resonance with the degeneracy order $j$ takes place. The topological structures of degenerate resonance zones and the problem of synchronization of oscillations when an invariant torus passes through a degenerate resonance zone with the degeneracy orders $j=2$ and $j=3$ have been well studied. |
| Keywords | pendulum equations, quasiperiodic nonconservative perturbations, degenerate resonance. |
| Citation | Kostromina O. S. ''On the conditions for the existence of degenerate resonance levels in pendulum equations under quasiperiodic nonconservative 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 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 119-124. Available at: https://conf.svmo.ru/files/2025/papers/paper24.pdf. - Date of access: 30.08.2025. |
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