Exponentially stable manifolds in
the neighbourhood of elliptic equilibria

by Antonio Giorgilli Daniele Muraro

**Abstract:**
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 FPU type.

preprint (2003)

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