most citedContinuations and bifurcations of relative equilibria for the positive curved three body problem

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math.DS2024

Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere

Toshiaki Fujiwara, Ernesto Pérez-Chavela, Shuqiang Zhu

We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body…

math.DS2024

Periodic orbits near collision in a restricted four-body problem for the eight choreography

Abimael Bengochea, Jaime Burgos-García, Ernesto Pérez-Chavela

We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influ…