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

Tomasz Kapela·Piotr Zgliczynski
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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.

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Tomasz Kapela, Piotr Zgliczynski. 2003-04-25. An existence of simple choreographies for N-body problem - a computer assisted proof. https://doi.org/10.1088/0951-7715%2F16%2F6%2F302

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