Effective stability in Hamiltonian systems in the
light of Nekhoroshev's theorem

by Antonio Giorgilli

**Abstract:**
The methods of classical perturbation theory are
revisited in the light of a rigorous algebraic approach and of
Nekhoroshev's theorem on stability over exponentially large times. The
applications to the restricted three body problem and to a statistical
model of a diatomic gas of identical molecules are illustrated, with the
aim of giving good estimates for the size of the stability region and
for the dependence on the number of degrees of freedom.

*Integrable systems and
applications*, M. Balabane, P. Lochak and C. Sulem eds.,
Lect. Notes in Phys. **342**, pp 142-153, Springer-Verlag (1988)

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