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

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

References in corpus (2)

• The Geometric Phase in the Three-Body Problem
• Periodic orbits for three particles with finite angular momentum

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