Exponentially stable manifolds in the neighbourhood of elliptic equilibria
We consider a Hamiltonian system in a neighbourhood of an elliptic equilibrium which is a minimum for the Hamiltonian. With appropriate non-resonance conditions we prove that in the neighbourhood of the equilibrium there exist low dimensional manifolds that are exponentially stable in Nekhoroshev’s sense. This generalizes the theorem of Lyapounov on the existence of periodic orbits. The result may be meaningful for, e.g., the dynamics of non-linear chains of the Fermi-Pasta-Ulam (FPU) type.