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? 



Reference Request: Siegel Center Problem
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. 


