Special Session 59: Central configurations, periodic solutions, variational method and beyond in celestial mechanics
Contents
We describe a simple variational principle for periodic solutions in Hamiltonian systems whose solutions correspond to elliptic stable periodic solutions. We use a variant of the Maslov index together with mountain pass geometry to characterize such periodic solutions. Applications in the the theory of exact symplectic period mappings for planar Hamiltonian systems are discussed. We also place this discussion in the context of periodic solutions of the N-body problem.