Polygonal homographic orbits in spaces of constant curvature

Details Polygonal homographic orbits in spaces of constant curvature Polygonal homographic orbits in spaces of constant curvature

2011-08-11

arxiv.org/abs/1108.2478v2

Mathematics

Dynamical Systems

Scientific paper

We prove that the geometry of the 2-dimensional $n$-body problem for spaces
of constant curvature $\kappa\neq 0$, $n\geq 3$, does not allow for polygonal
homographic solutions, provided that the corresponding orbits are irregular
polygons of non-constant size.

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