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 Mosc. Math. J., 2003, Volume 3, Number 3, Pages 1039–1052 (Mi mmj120)

On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations

Space Research Institute, Russian Academy of Sciences

Abstract: A system which differs from an integrable Hamiltonian system with two degrees of freedom by a small Hamiltonian perturbation and much a smaller non-Hamiltonian perturbation is considered. The unperturbed system is isoenergetically nondegenerate. The averaging method is used for an approximate description of solutions of the exact system on a time interval inversely proportional to the amplitude of the non-Hamiltonian perturbation. The error of this description (averaged over initial conditions) is estimated from above by a value proportional to the square root of the amplitude of the Hamiltonian perturbation.

Key words and phrases: Perturbation theory, averaging method.

DOI: https://doi.org/10.17323/1609-4514-2003-3-3-1039-1052

Full text: http://www.ams.org/.../abst3-3-2003.html
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MSC: Primary 14P25, 57M25; Secondary 14H20, 53D99
Received: October 14, 2002; in revised form July 7, 2003
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Citation: A. I. Neishtadt, “On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations”, Mosc. Math. J., 3:3 (2003), 1039–1052

Citation in format AMSBIB
\Bibitem{Nei03} \by A.~I.~Neishtadt \paper On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations \jour Mosc. Math.~J. \yr 2003 \vol 3 \issue 3 \pages 1039--1052 \mathnet{http://mi.mathnet.ru/mmj120} \crossref{https://doi.org/10.17323/1609-4514-2003-3-3-1039-1052} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2078572} \zmath{https://zbmath.org/?q=an:1062.70046} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208594300013} 

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• http://mi.mathnet.ru/eng/mmj/v3/i3/p1039

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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2. Simo C., Vieiro A., “Planar radial weakly dissipative diffeomorphisms”, Chaos, 20:4 (2010), 043138
3. Fejoz J., “On “Arnold's Theorem” on the Stability of the Solar System”, Discret. Contin. Dyn. Syst., 33:8 (2013), 3555–3565
4. Guzzo M., Lega E., “The Numerical Detection of the Arnold Web and its Use for Long-Term Diffusion Studies in Conservative and Weakly Dissipative Systems”, Chaos, 23:2 (2013), 023124
5. A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843