Periodic orbits for the planar Newtonian three-body problem coming from the elliptic restricted three-body problems

Llibre, J.; Saari, D.G.

Transactions of the American Mathematical Society 347(8): 3017-3030


ISSN/ISBN: 0002-9947
Accession: 086541959

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Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar three-body problem.