Chapter

Integrable Systems and Applications

Volume 342 of the series Lecture Notes in Physics pp 142-153

Date:

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

  • Antonio GiorgilliAffiliated withDipartimento di Matematica dell'Università

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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.