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Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.
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What is an integrable system?
I'll take off from the questioner's suggesting that maybe it's better to say what is a NON-integrable system is.
The Newtonian planar three body problem, for most masses, has been proven to be non-in …
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