Triple collision in the planar isosceles three body problem

Devaney, R.L.

Inventiones Mathematicae 60(3): 249-267

1980


ISSN/ISBN: 0020-9910
Accession: 089193433

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Abstract
We employ a device due to Mc Gehee 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".