Polygonal homographic orbits in spaces of constant curvature

Tibboel, Pieter

doi:10.1090/S0002-9939-2012-11410-8

Polygonal homographic orbits in spaces of constant curvature
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Proc. Amer. Math. Soc. 141 (2013), 1465-1471 Request permission

Abstract:

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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