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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