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On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories. (English) Zbl 0492.70018

MSC:
70H05 Hamilton’s equations
34C25 Periodic solutions to ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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[1] \scA. Ambrosetti and G. Mancini, Solutions of minimal period for a class of convex Hamiltonian systems, Math. Ann., in press. · Zbl 0466.70022
[2] \scF. Clarke, Periodic solutions to Hamiltonian inclusions, J. Differential Equations, in press. · Zbl 0461.34030
[3] Clarke, F; Ekeland, I, Hamiltonian trajectories having prescribed minimal period, Comm. pure appl. math., 33, 103-116, (1980) · Zbl 0403.70016
[4] Ekeland, I, Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, J. differential equations, 34, 523-534, (1979) · Zbl 0446.70019
[5] \scI. Ekeland and J. M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Ann. of Math., in press. · Zbl 0449.70014
[6] Fadell, E; Rabinowitz, P.H, Generalized cohomological index theories for group actions with an application to bifurcation questions for Hamiltonian systems, Invent. math., 45, 139-174, (1978) · Zbl 0403.57001
[7] Liapunov, A, Problème général de la stabilité du mouvement, Ann. fac. sci. Toulouse, 2, 203-474, (1907) · JFM 38.0738.07
[8] Moser, J, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. pure appl. math., 29, 727-747, (1976) · Zbl 0346.34024
[9] Rabinowitz, P.H, Periodic solutions of Hamiltonian systems, Comm. pure appl. math., 31, 157-184, (1978) · Zbl 0358.70014
[10] Rabinowitz, P.H, A variational method for finding periodic solutions of differential equations, () · Zbl 0152.10003
[11] Weinstein, A, Normal modes for nonlinear Hamiltonian systems, Invent. math., 20, 47-57, (1973) · Zbl 0264.70020
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