We review some recently discovered periodic orbits of the N-body problem, whose existence is proved by means of variational methods. These orbits are minimizers of the Lagrangian action functional in a set of $T$-periodic loops, equivariant for the action of a group $G$ and satisfying some topological constraints. Both the group action and the topological constraints are defined using the symmetry of Platonic polyhedra.

Periodic orbits of the N-body problem with the symmetry of platonic polyhedra.

GRONCHI, GIOVANNI FEDERICO
2014-01-01

Abstract

We review some recently discovered periodic orbits of the N-body problem, whose existence is proved by means of variational methods. These orbits are minimizers of the Lagrangian action functional in a set of $T$-periodic loops, equivariant for the action of a group $G$ and satisfying some topological constraints. Both the group action and the topological constraints are defined using the symmetry of Platonic polyhedra.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/585470
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