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