Year: 1982

Authors: G. Gallavotti

Title: A Criterion of Integrability for Perturbed Nonresonant Harmonic Oscillators. "Wick Ordering" of the Perturbations in Classical Mechanics and Invariance of the Frequency Spectrum
Communication in Mathematical Physics, 87, 365-383, 1982

Abstract: We introduce an analogue to the renormalization theory (of quantum fields) into classical mechanics. We also find an integrability criterion guaranteeing the convergence of Birkhoff s series and an algorithm for modifying the hamiltonian to fix the frequency spectrum of the quasi-periodic motions. We point out its possible relevance to the transition to chaos.

Key words:  Classical Mechanics, Integrability, Counterterms, Perturbation theory