An existence of simple choreographies for N-body problem - a computer assisted proof

Details An existence of simple choreographies for N-body problem - a computer assisted proof An existence of simple choreographies for N-body problem - a computer assisted proof

2003-04-25

arxiv.org/abs/math/0304404v1

Mathematics

Dynamical Systems

19 pages, 9 figures

Scientific paper

10.1088/0951-7715/16/6/302

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.

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