An existence proof of a symmetric periodic orbit in the octahedral six-body problem

Preprint English OPEN
Cavalcanti, Anete Soares (2016)
  • Subject: Mathematics - Dynamical Systems

We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the Lagrangian action functional on a well chosen class of symmetric loops.
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