Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 215–225 | Cite as

Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem

  • Urs FrauenfelderEmail author
  • Lei Zhao


In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering problems. In this article, using Floer homology, we show that there is either a periodic collisional orbit, or there are infinitely many consecutive collision orbits in the planar circular restricted three-body problem on each bounded component of the energy hypersurface for Jacobi energy below the first critical value.



Urs Frauenfelder is partially supported by the grant DFG FR/2637/2-1 funded by the Deutsche Forschungsgemeinschaft (DFG) and Lei Zhao is supported by the grants DFG FR/2637/2-1 and DFG ZH 605/1-1.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of AugsburgAugsburgGermany

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