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Does anyone have a reference to where I may find a statement of the problem and perhaps (but not required) some elementary dicussion of Siegel's Center Problem?

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  • $\begingroup$ Siegel's own book Lectures on celestial mechanics is a good source. There is an English translation. $\endgroup$
    – Alexandre Eremenko
    Commented Feb 27, 2018 at 12:59

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Try this references: http://aip.scitation.org/doi/abs/10.1063/1.525964 (A simple proof of a particular case of C. Siegel’s center theorem, by R. de la Llave) and http://www.math.osu.edu/~costin.10/950/tutorial_KAM.pdf (A tutorial on KAM theory, by the same author).

Also the following book "The KAM story: a friendly introduction to the content, history, and significance of classical Kolmogorov-Arnold- Moser theory" by H.S. Dumas has a nice historical overview of the Siegel's center and related problems.

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