On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories

DOI10.1016/0022-0396(82)90093-6zbMath0492.70018OpenAlexW2014496566MaRDI QIDQ1168090

Giovanni Mancini, Antonio Ambrosetti

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0022-0396(82)90093-6

zbMATH Keywords

free critical pointsperiodic Hamiltonian trajectoriesperiodic solutions with prescribed minimal periodsuper-quadratic Hamiltonian systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (13)

On the number of periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Closed characteristics on asymmetric convex hypersurfaces in \(\mathbb{R}^{2n}\) and the corresponding pinching conditions ⋮ Convex Hamiltonian energy surfaces and their periodic trajectories ⋮ A note on the existence of multiple brake orbits ⋮ The brake orbits of Hamiltonian systems on positive-type hypersurfaces ⋮ Infinite dimensional local linking and some applications to the Hamiltonian systems ⋮ Critical points and nonlinear variational problems ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ Applications numériques de la dualité en mécanique hamiltonienne ⋮ Periodic solutions of nonlinear vibrating strings and duality principles ⋮ Existence of multiple normal mode trajectories on convex energy surfaces of even, classical Hamiltonian systems ⋮ Multiple homoclinic orbits for a class of conservative systems ⋮ Existence of homoclinic orbits to invariant tori of Hamiltonian systems: a model case

Cites Work

• Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz
• On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
• Periodic solutions to Hamiltonian inclusions
• Solutions of minimal period for a class of convex Hamiltonian systems
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• Normal modes for nonlinear Hamiltonian systems
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Periodic solutions of hamiltonian systems
• Hamiltonian trajectories having prescribed minimal period
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations

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