On nonlinear motions of a Hamiltonian system in the case of external resonance

DOI10.1016/S0034-4877(02)80013-1zbMath1016.37027MaRDI QIDQ1853804

Boris S. Bardin

Publication date: 22 January 2003

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

stabilityperiodic solutionsnonlinear oscillationsnormal formsKAM theoryHamiltonian systemperturbation with external resonance

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nonlinear resonances for nonlinear problems in mechanics (70K30) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Cites Work

• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• The motion of a system close to Hamiltonian with one degree of freedom when there is resonance in forced vibrations
• Periodic solutions of nearly Lyapunov system in the external resonance case
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