Abstract
A new regularizing transformation for the three-dimensional restricted three-body problem is constructed. It is explicitly derived and is equivalent to a simple rational map. Geometrically it is equivalent to a rotation of the 3-sphere. Unlike the KS map it is dimension preserving and is valid inn dimensions. This regularizing map is applied to the restricted problem in order to prove the existence of a family of periodic orbits which continue from a family of collision orbits.
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Belbruno, E.A. A new regularization of the restricted three-body problem and an application. Celestial Mechanics 25, 397–415 (1981). https://doi.org/10.1007/BF01234179
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DOI: https://doi.org/10.1007/BF01234179