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In this article we consider the existence of a family of doubly-symmetricperiodic orbits in the spatial circular Hill's lunar problem, in which thesecondary primary at the origin is oblate. The existence is shown by applying afixed point theorem to the equations with periodical conditions expressed inPoincare-Delaunay elements for the double symmetries after eliminating theshort periodic effects in the first-order perturbations of the approximatedsystem.

Doubly-symmetric periodic orbits in the spatial Hill's lunar problem with oblate secondary primary