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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. University of Augsburg, Augsburg, Germany

    Urs Frauenfelder & Lei Zhao

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  1. Urs Frauenfelder
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  2. Lei Zhao
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Correspondence to Urs Frauenfelder.

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Frauenfelder, U., Zhao, L. Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem. Math. Z. 291, 215–225 (2019). https://doi.org/10.1007/s00209-018-2080-7

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  • DOI: https://doi.org/10.1007/s00209-018-2080-7

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