Some remarks on symmetric periodic orbits in the restricted three-body problem

摘要

The planar circular restricted three body problem (PCRTBP) is symmetric withrespect to the line of masses and there is a corresponding anti-symplecticinvolution on the cotangent bundle of the 2-sphere in the regularized PCRTBP.Recently it was shown that each bounded component of an energy hypersurfacewith low energy for the regularized PCRTBP is fiberwise starshaped. This enableus to define a Lagrangian Rabinowitz Floer homology which is related toperiodic orbits symmetric for the anti-symplectic involution in the regularizedPCRTBP and hence to symmetric periodic orbits in the unregularized problem. Inthis paper we compute of this homology and discuss about symmetric periodicorbits.