On nonlinear motions of Hamiltonian system in case of fourth order resonance

DOI10.1134/S156035470701008XzbMath1229.34052MaRDI QIDQ655246

Boris S. Bardin

Publication date: 3 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsnormal formKAM theoryHamiltonian systemresonanceaction-angle variables

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (7)

Nonlinear oscillations of a 1:1 resonance Hamiltonian system ⋮ Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem ⋮ Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite ⋮ Unnamed Item ⋮ On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance ⋮ A study of the motions of an autonomous Hamiltonian system at a 1:1 resonance ⋮ Lyapunov orbits in the \(n\)-vortex problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
• On motions near the Lagrange equilibrium point \(L_4\) in the case of Routh's critical mass ratio
• A new class of periodic solutions in the restricted three body problem
• Families of periodic solutions near a Hamiltonian equilibrium when the ratio of two eigenvalues is 3
• Lyapunov's center theorem for resonant equilibrium
• Periodic solutions near a resonant equilibrium of a Hamiltonian system
• Periodic orbits emanating from a resonant equilibrium

This page was built for publication: On nonlinear motions of Hamiltonian system in case of fourth order resonance