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

This article is cited in 5 scientific papers (total in 5 papers)

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

A. I. Neishtadt

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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Bibliographic databases:

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
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\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
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\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}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Celletti A., Froeschle C., Lega E., “Dissipative and weakly-dissipative regimes in nearly-integrable mappings”, Discrete and Continuous Dynamical Systems, 16:4 (2006), 757–781  crossref  mathscinet  isi
    2. Simo C., Vieiro A., “Planar radial weakly dissipative diffeomorphisms”, Chaos, 20:4 (2010), 043138  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Fejoz J., “On “Arnold's Theorem” on the Stability of the Solar System”, Discret. Contin. Dyn. Syst., 33:8 (2013), 3555–3565  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  elib
    5. A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Moscow Mathematical Journal
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