A perturbation theory near convex Hamiltonian systems

DOI10.1016/0022-0396(83)90069-4zbMath0476.34035OpenAlexW1970992192MaRDI QIDQ1160334

Ivar Ekeland

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0022-0396(83)90069-4

zbMATH Keywords

bifurcationasymptotic expansions near isolated closed orbitsbifurcations of continuous families of closed orbitsdual action functionalWeinstein's theorem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Hamilton's equations (70H05)

Related Items (11)

Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems ⋮ Symmetry breaking in Hamiltonian systems ⋮ Periodic perturbations of Hamiltonian systems ⋮ Perturbation of planar, keplerian Hamiltonian systems ⋮ Periodic solutions of a class of Hamiltonian systems with singularities ⋮ Perturbed Keplerian Hamiltonian systems ⋮ Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori ⋮ Coupling linearity and twist: an extension of the Poincaré-Birkhoff theorem for Hamiltonian systems ⋮ Non-convex self-dual Lagrangians: new variational principles of symmetric boundary value problems ⋮ Bifurcation of homoclinic orbits for Hamiltonian systems ⋮ Periodic solutions of nonlinear vibrating strings and duality principles

Cites Work

• Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz
• Periodic solutions to Hamiltonian inclusions
• Bifurcation from simple eigenvalues
• Normal modes for nonlinear Hamiltonian systems
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Hamiltonian trajectories having prescribed minimal period
• Regularization of kepler's problem and the averaging method on a manifold
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