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

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  • The planar circular restricted three-body problem (PCRTBP) is symmetric with respect to the line of masses and there is a corresponding anti-symplectic involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP. Recently it turned out that each bounded component of an energy hypersurface with low energy for the regularized PCRTBP is fiberwise starshaped. This enables us to define a Lagrangian Rabinowitz Floer homology which is related to periodic orbits symmetric for the anti-symplectic involution in the regularized PCRTBP and hence to symmetric periodic orbits in the unregularized problem. We compute this homology and discuss the properties of the symmetric periodic orbits.
    Mathematics Subject Classification: Primary: 58F05, 58E05; Secondary: 53C35.

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