Critical points at infinity of the 3-body Problem in $\mathbb{R}^4$

Abstract

We show that critical points at infinity in the 3-body problem in $\mathbb{R}^4$ do not realize the infimum of the energy. This completes our previous work [Journal of Geometric Mechanics, 12, pp323-341 (2020), doi:10.3934/jgm.2020012] on the existence of Lyapunov stable relative periodic orbits in the 3-body problem in $\mathbb{R}^4$.Comment: 6 pages, 1 figur