Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point
by Antonio Giorgilli

Abstract: The classical problem of the direct construction of integrals for a Hamiltonian system in the neighbourhood of an elliptic equilibrium point is revisited in the light of the rigorous Nekhoroshev's like theory. It is shown how the results about stability over exponentially large times can be recovered in a simple and effective way, at least in the nonresonant case, and in fact even more conveniently than with the usual indirect method involving normalizing canonical transformations. An application is also made to the problem of the freezing of the harmonic actions in classical models.

Ann. Ist. H. Poincaré, 48, n. 4, 423-439 (1988)

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