Algebraic proof of the non-integrability of Hill's problem
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Hill's lunar problem appears in celestial mechanics as a limit of the restricted three-body problem. It is parameter-free and thus globally far from any simple well-known problem, and has shed strong numerical evidence of its lack of integrability in the past. An algebraic proof of meromorphic non-integrability is presented here. Beyond the result itself, the paper can also be considered as an example of the application of differential Galois and Morales–Ramis theories to a significant problem.
|Number of pages||20|
|Journal||Ergodic Theory and Dynamical Systems|
|Publication status||Published - 2005|
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