Long periodic orbits near an equilibrium and the averaging method in higher-order resonances

DOI10.1016/0022-0396(84)90109-8zbMath0527.34044OpenAlexW1988257133MaRDI QIDQ786300

Hidekazu Ito

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(84)90109-8

zbMATH Keywords

periodic orbitsHamiltonian systemsaveraging methodsgeometrical distributionLyapunov non- resonance conditions

Mathematics Subject Classification ID

Hamilton's equations (70H05) Averaging method for ordinary differential equations (34C29)

Related Items

Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems

Cites Work

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• Lagrangian submanifolds and Hamiltonian systems
• Long periodic solutions near an equilibrium in general resonance cases
• Bifurcations and Hamilton's principle
• Hopf's bifurcation theorem and the center theorem of Liapunov with resonance cases
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• On the periodic motions near a given periodic motion of a dynamical system
• A unifying theory in determining periodic families for Hamiltonian systems at resonance
• A new class of periodic solutions in the restricted three body problem
• Lyapunov's center theorem for resonant equilibrium
• Normal modes for nonlinear Hamiltonian systems
• Symplectic v‐manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Regularization of kepler's problem and the averaging method on a manifold