Periodic solutions and regularization of a Kepler problem with time-dependent perturbation

We consider a Kepler problem in dimension two or three with a time-dependent T-periodic perturbation. We prove that for any prescribed positive integer N, there exist at least N periodic solutions (with period T) as long as the perturbation is small enough. Here the solutions are understood in a gen...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019, Vol.372 (1), p.677-703
Main Authors: Boscaggin, Alberto, Ortega, Rafael, Zhao, Lei
Format: Article
Language:English
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Summary:We consider a Kepler problem in dimension two or three with a time-dependent T-periodic perturbation. We prove that for any prescribed positive integer N, there exist at least N periodic solutions (with period T) as long as the perturbation is small enough. Here the solutions are understood in a general sense as they are allowed to have collisions. The concept of generalized solutions is defined intrinsically, and it coincides with the notion obtained in celestial mechanics via the theory of regularization of collisions.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7589