A criterion of integrability for perturbed nonresonant harmonic oscillators. ?Wick ordering? of the perturbations in classical mechanics and invariance of the frequency spectrum | Zendy

Giovanni Gallavotti | Zendy

Open Access

A criterion of integrability for perturbed nonresonant harmonic oscillators. ?Wick ordering? of the perturbations in classical mechanics and invariance of the frequency spectrum

Author(s) -

Giovanni Gallavotti

Publication year - 1982

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/bf01206029

Subject(s) - harmonic oscillator , renormalization , mathematics , hamiltonian (control theory) , hamiltonian system , spectrum (functional analysis) , statistical mechanics , classical mechanics , mathematical physics , physics , quantum mechanics , statistical physics , mathematical optimization

We introduce an analogue to the renormalization theory (of quantum fields)into classical mechanics. We also find an integrability criterionguaranteeing the convergence of Birkhoff's series and an algorithm formodifying the Hamiltonian to fix the frequency spectrum of thequasi-periodic motions. We point out its possible relevance to thetransition to chaos

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