Summary
We show how to construct a classical perturbation theory at any finite order for an Hamiltonian system describing a chain of weakly coupled rotators, both for the nonresonant and for the resonant cases. In particular, by means of a suitable algebraic scheme, we show how small denominantors and propagation of harmonics can be controlled.
Riassunto
Si mostra come si costruisce una teoria classica delle perturbazioni per un sistema Hamiltoniano che descrive una catena di rotatori debolmente accoppiati, sia nel caso non risonante che nel caso risonante. In particolare, mediante un opportuno schema algebrico, si mostra come si controllano i piccoli denominatori e la propagazione delle armoniche.
Резюме
Мы показываем, как конструируется классическая теория возмущений в любом порядке для гамильтоновой системы, описывающей цепочку слабо связанных ротаторов, в резонансном и нерезонансном случаях. В частности, с помощью соответствующей алгебраческой схемы мы показываем, как можно описывать малые знаменатели и распространение гармоник.
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Benettin, G., Galgani, L. & Giorgilli, A. Classical perturbation theory for systems of weakly coupled rotators. Nuov Cim B 89, 89–102 (1985). https://doi.org/10.1007/BF02723539
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DOI: https://doi.org/10.1007/BF02723539