The behaviour of a nonlinear Hamiltonian system with one degree of freedom at the boundary of a parametric resonance domain

DOI10.1016/0021-8928(95)00063-1zbMath0900.70220OpenAlexW1991369176MaRDI QIDQ1369904

Anatoliy P. Markeev

Publication date: 4 November 1997

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(95)00063-1

zbMATH Keywords

equilibriumperturbed systemstochastic behaviourexistence of stable periodic motionsnonlinear oscillation frequencies

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Cites Work

• Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
• On stability of a non-autonomous Hamiltonian system in parametric resonance of dominant mode
• Asymptotic solutions of Hamiltonian systems with first-order resonance
• Third-order resonance in a Hamiltonian system with one degree of freedom
• Stability of planar oscillations of a satellite in an elliptic orbit
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