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I intend to learn KAM Theory. Could you please suggest me a good book on KAM Theory to begin with, where main results are discussed with complete proofs. Thank you.

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There are many good books. I can recommend two:

  1. S. Sternberg, Celestial mechanics, Part 2, W. A. Benjamin Inc., NY 1969

  2. V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, there are two English translations. The original Russian title is "Additional chapters of the theory of differential equations".

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  • MR1997070 Kappeler, Thomas(CH-ZRCH); Pöschel, Jürgen(D-STGTMP) KdV & KAM. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 45. Springer-Verlag, Berlin, 2003. xiv+279 pp.
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There is a nice recent book H Scott Dumas: The KAM Story. World Scientific 2014. It does not go very deep but it is, as the subtitle says, a friendly introduction. I guess it might be a beneficial supplementary source in studying the KAM theory as there is a lot of its history and motivation presented.

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