04-111 Juan J. Morales-Ruiz, Carles Sim , Sergi Simon

Algebraic proof of the non-integrability of Hill's Problem (616K, Postscript) Apr 15, 04

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Abstract. Hill's lunar problem appears in Celestial Mechanics as a limit of the Restricted Three-Body Problem. Besides, information on the former shows light on several other three-body problems. It contains no parameters and is globally far from any simple well-known problem. Strong numerical evidences of its lack of integrability have been given in the past. Here an algebraic proof of non-integrability is presented. Beyond the result in itself, the paper can also be considered as an example of the application of differential Galois theory to a significant problem.

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