On three-dimensional systems close to integrable ones

Title	On three-dimensional systems close to integrable ones
Authors	K. E. Morozov¹ ¹Ufa University of Science and Technology
Annotation	At present, nonconservative perturbations of two-dimensional Hamiltonian systems have been studied quite thoroughly. This paper considers the generalization of this theory to the three-dimensional case, where the unperturbed system is nonlinear, integrable and has a region filled with closed phase trajectories. In the case of autonomous perturbations, the main focus is on the problem of limit cycles. Two systems are considered as examples: the Van der Pol equation with automatic frequency control and the Lorenz system in the case of large Rayleigh numbers. For non-autonomous perturbations, the investigation involves resonance analysis and deriving an averaged system that determines the dynamics in the resonance zone.
Keywords	perturbations, averaging, limit cycles, resonances.
Citation	Morozov K. E. ''On three-dimensional systems close to integrable ones'' [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. 185-192. Available at: https://conf.svmo.ru/files/2025/papers/paper37.pdf. - Date of access: 30.08.2025.