Periodic solutions of Hamilton’s equations and local minima of the dual action

Source abstract

The dual action is a functional whose extremals lead to solutions of Hamilton’s equations. Up to now, extremals of the dual action have been obtained either through its global minimization or through application of critical point theory. A new methodology is introduced in which local minima of the dual action are found to exist. Applications are then made to the existence of Hamiltonian trajectories having prescribed period.