# American Institute of Mathematical Sciences

2015, 2015(special): 1115-1124. doi: 10.3934/proc.2015.1115

## Classification of periodic orbits in the planar equal-mass four-body problem

 1 School of Mathematics and System Science, Beihang University, Beijing 100191, China 2 Department of Mathematics, Brigham Young University, Provo, Utah 84602 3 Department of Mathematics and Computer Science, Virginia State University, Petersburg, Virginia 23806

Received  September 2014 Revised  April 2015 Published  November 2015

In the N-body problem, many periodic orbits are found as local Lagrangian action minimizers. In this work, we classify such periodic orbits in the planar equal-mass four-body problem. Specific planar configurations are considered: line, rectangle, diamond, isosceles trapezoid, double isosceles, kite, etc. Periodic orbits are classified into 8 categories and each category corresponds to a pair of specific configurations. Furthermore, it helps discover several new sets of periodic orbits.
Citation: Duokui Yan, Tiancheng Ouyang, Zhifu Xie. Classification of periodic orbits in the planar equal-mass four-body problem. Conference Publications, 2015, 2015 (special) : 1115-1124. doi: 10.3934/proc.2015.1115
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