On the periodic orbits and the integrability of the regularized Hill lunar problem

Agraïments: The second author is partially supported by CAPES/MECD-DGU 015/2010 Brazil and Spain, process number BEX 4251/10-5.The classical Hill's problem is a simplified version of the restricted three-body problem where the distance of the two massive bodies (say, primary for the largest one and secondary for the smallest) is made infinity through the use of Hill's variables. The Levi-Civita regularization takes the Hamiltonian of the Hill lunar problem into the form of two uncoupled harmonic oscillators perturbed by the Coriolis force and the Sun action, polynomials of degree 4 and 6, respectively. In this paper we study periodic orbits of the planar Hill problem using the averaging theory. Moreover we provide information about the C1 integrability or non-integrability of the regularized Hill lunar problem