Resonant Lyapunov families of periodic motions of reversible systems

DOI10.1016/S0021-8928(04)00048-6zbMath1122.70342OpenAlexW2038990259MaRDI QIDQ3378111

V. N. Tkhai

Publication date: 30 March 2006

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

Full work available at URL: https://doi.org/10.1016/s0021-8928(04)00048-6

zbMATH Keywords

reversible systemperiodic motionsLyapunov families

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Complex behavior and chaotic systems of ordinary differential equations (34C28) Nonlinear resonances for nonlinear problems in mechanics (70K30)

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Cites Work

• Reversible systems
• The reversibility of mechanical systems
• Families of periodic solutions near a Hamiltonian equilibrium when the ratio of two eigenvalues is 3
• An extension to resonant cases of Liapunov's theorem concerning the periodic solutions near a Hamiltonian equilibrium
• Periodic solutions for dynamical systems possessing a first integral in the resonance case
• Lyapunov's center theorem for resonant equilibrium
• Periodic solutions near a resonant equilibrium of a Hamiltonian system
• Cycle in a system close to a resonance system
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