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Generalized periodic orbits of the time-periodically forced Kepler problem accumulating at the center and of circular and elliptic restricted three-body problems

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In this paper, we consider a time-periodically forced Kepler problem in any dimension, with an external force which we only assume to be regular in a neighborhood of the attractive… Click to show full abstract

In this paper, we consider a time-periodically forced Kepler problem in any dimension, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic orbits in this system, with possible double collisions with the center regularized, which accumulate at the attractive center. The result is obtained via a localization argument combined with a result on $$C^{1}$$ C 1 -persistence of closed orbits by a local homotopy-stretching argument. Consequently, by formulating the circular and elliptic restricted three-body problems of any dimension as time-periodically forced Kepler problems, we obtain that there exist infinitely many periodic orbits, with possible double collisions with the primaries regularized, accumulating at each of the primaries.

Keywords: periodically forced; center; time periodically; forced kepler; periodic orbits

Journal Title: Mathematische Annalen
Year Published: 2021

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