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- Q587081 subject Q11157523.
- Q587081 subject Q7464082.
- Q587081 abstract "The Kolmogorov–Arnold–Moser theorem (KAM theorem) is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics.The problem is whether or not a small perturbation of a conservative dynamical system results in a lasting quasiperiodic orbit. The original breakthrough to this problem was given by Andrey Kolmogorov in 1954. This was rigorously proved and extended by Vladimir Arnold (in 1963 for analytic Hamiltonian systems) and Jürgen Moser (in 1962 for smooth twist maps), and the general result is known as the KAM theorem. The KAM theorem, as it was originally stated, could not be applied directly as a whole to the motions of the solar system because of the presence of degeneracy in the unperturbed Kepler problem. However, it is useful in generating corrections of astronomical models, and to prove long-term stability and the avoidance of orbital resonance in solar system. Arnold used the methods of KAM to prove the stability of elliptical orbits in the planar three-body problem.".
- Q587081 wikiPageExternalLink kam-1.pdf.
- Q587081 wikiPageExternalLink mpa?yn=01-29.
- Q587081 wikiPageExternalLink kolmo100.pdf.
- Q587081 wikiPageExternalLink KAM_theory_in_celestial_mechanics.
- Q587081 wikiPageExternalLink 8955_chap01.pdf.
- Q587081 wikiPageExternalLink 8955.
- Q587081 wikiPageWikiLink Q1000646.
- Q587081 wikiPageWikiLink Q10886678.
- Q587081 wikiPageWikiLink Q11157523.
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- Q587081 wikiPageWikiLink Q7464082.
- Q587081 wikiPageWikiLink Q822938.
- Q587081 wikiPageWikiLink Q842160.
- Q587081 comment "The Kolmogorov–Arnold–Moser theorem (KAM theorem) is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics.The problem is whether or not a small perturbation of a conservative dynamical system results in a lasting quasiperiodic orbit. The original breakthrough to this problem was given by Andrey Kolmogorov in 1954.".
- Q587081 label "Kolmogorov–Arnold–Moser theorem".