Algebraic proof of the non-integrability of Hill's problem

J. Morales-Ruiz, C. Simo, Sergi Simon

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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.
Original languageEnglish
Pages (from-to)1237-1256
Number of pages20
JournalErgodic Theory and Dynamical Systems
Issue number4
Publication statusPublished - 2005


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