an:03866646
Zbl 0544.70026
Gallavotti, Giovanni
A criterion of integrability for perturbed nonresonant harmonic oscillators. ''Wick Ordering'' of the perturbations in classical mechanics and invariance of the frequency spectrum
EN
Commun. Math. Phys. 87, 365-383 (1982).
00147572
1982
j
70H05 37J35 37K10
Wick ordering; invariance of the frequency spectrum; perturbations of integrable Hamiltonian systems; n degree of freedom; theorem of Poincar??; generic nonexistence of analytic integrals; renormalization
The paper studies perturbations of integrable Hamiltonian systems of n degree of freedom. The results pertain to the famous theorem of Poincar?? on the generic nonexistence of analytic integrals for perturbed Hamiltonians. The author introduces the notion of ''renormalization'' in this setting. Among other results he proves the following. There is at most one renormalization of the perturbed Hamiltonian which is canonically analytically conjugate to the unperturbed one. He also gives a criterion for the existence of such renormalization.
E.Gutkin