Abstract
We employ a device due to McGehee to discuss the qualitative behavior of orbits which reach or come close to triple collision in a special case of the planar three body problem. We show that there exist infinitely many orbits which both begin and end in triple collision. Nearby orbits behave in different ways depending on whether they pass close to the collinear or equilateral triangle central configuration. Finally, we discuss a new type of orbit in the three body problem which we call “billiard shots”.
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Partially supported by NSF Grant MCS 79-00430.
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Devaney, R.L. Triple collision in the planar isosceles three body problem. Invent Math 60, 249–267 (1980). https://doi.org/10.1007/BF01390017
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DOI: https://doi.org/10.1007/BF01390017