Minimax arguments have been used for the construction of closed orbits in Hamiltonian systems with starshaped energy surfacesFloer introduced a new approach to Morse theory which allowed him to prove the Arnol'd conjecture in many cases; the complete conjecture was proved by several groups of people. Further developments involve the variational study of closed characteristics on contact manifolds.

Variational methods have been used in varying degrees of abstractness and generality to construct so-called chaotic solutions or ìmultibump solutionsî in Hamiltonian systems, and in Lagrangian systems (monotone twist maps of an annulus being the simplest example.)