An existence of simple choreographies for N-body problem - a computer assisted proof
arXiv:math/0304404 · doi:10.1088/0951-7715/16/6/302
Abstract
We consider a question of finding a periodic solution for the planar Newtonian N-body problem with equal masses, where each body is travelling along the same closed path. We provide a computer assisted proof for the following facts: local uniqueness and convexity of Chenciner and Montgomery Eight, an existence (and local uniqueness) for Gerver's SuperEight for 4-bodies and a doubly symmetric linear chain for 6-bodies.
19 pages, 9 figures