A criterion of integrability for perturbed nonresonant harmonic oscillators. ''Wick Ordering'' of the perturbations in classical mechanics and invariance of the frequency spectrum (Q797009)

The paper studies perturbations of integrable Hamiltonian systems of n degree of freedom. The results pertain to the famous theorem of Poincaré 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.