Abstract
Near a symmetric periodic orbit of the plane circular or elliptic restricted probelm, the conditions for a symmetric periodic orbit of the plane general three body problem are reduced, under a natural nondegeneracy condition, to the vanishing of a single real valued function. The implicit function theorem and Hörmander's generalized Morse's lemma are then used to analyze the set of zeros of this function.
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Kammeyer, P.C. Periodic three body orbits in the case of small third mass. Celestial Mechanics 17, 121–125 (1978). https://doi.org/10.1007/BF01371323
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DOI: https://doi.org/10.1007/BF01371323