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Recent advances in the study of the existence of periodic orbits of Hamiltonian systems.- The direct method in the study of periodic solutions of Hamiltonian systems with prescribed period.- Periodic solutions of Hamiltonian systems having prescribed minimal period.- Duality in non convex variational problems.- La theorie de la seconde variation et le probleme lineaire quadratique.- Methodes asymptotiques dans letude de systemes hamiltoniens non autonomes.- Numerical research of periodic solutions for a Hamiltonian system.