Rigorous estimates for the series expansions of Hamiltonian perturbation theory View Full Text


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Article Info

DATE

1985-10

AUTHORS

Antonio Giorgilli, Luigi Galgani

ABSTRACT

In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory, i.e. series expansions in the “small parameter” ε. For any order of normalization, we give a lower bound ɛ*r for the convergence radius of the normalized Hamiltonian, and a greater bound for the remainder, i.e. the non normalized part of the Hamiltonian. As an application, we consider the case of weakly coupled harmonic oscillators with highly nonresonant frequencies and show how, by optimizing, for fixed ε, the orderr of normalization, one gets for the remainder a greater bound of the formAe−(ɛ*1/ɛ)a, with positive constantsA,a and ɛ1* exponential estimate of Nekhoroshev's type. More... »

PAGES

95-112

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01230921

DOI

http://dx.doi.org/10.1007/bf01230921

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020743826


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