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| Many periodic orbits were discovered as local action minimizers in the N-body problem. A natural question is how to classify these periodic orbits. In this talk, we present our variational method and apply it to classify them in the planar equal-mass four-body problem. Specific planar configurations are considered: collinear shape, rectangle, diamond, trapezoid, double isosceles, kite, etc. The classification of these periodic orbits is based on pairs of different special configurations an orbit passing. It only includes 8 categories and each category corresponds to two different special configurations. Furthermore, it helps find several new sets of periodic orbits. |
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