Hamiltonian systems as selfdual equations

Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action functionals obtained by a generalization of Bogomolnyi’s trick of ‘dcompleting squares’. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.