SEMINAIRE MERCREDI 28 AVRIL 2004 14 heures Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Carles Simo Dept Matematica Aplicada i Analisi, Univ Barcelona Title: Algebraic proof of the non-integrability of Hill's Problem 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. An algebraic proof of non--integrability is presented. Beyond the result in itself, this result can also be considered as an example of the application of differential Galois theory to a significant problem. This is a joint work with Juan J. Morales-Ruiz and Sergi Simon