On the Dziobek configurations of the restricted \((N+1)\)-body problem with equal masses (Q1006280)

The author studies symmetry and finiteness of special central configurations. Namely, the author investigates an extention of \((N+1)\)-body central configurations with \(N\) bodies of equal masses, called Dziobek configurations. The results show that the extended configurations are highly symmetrical, and the proof is elementary in comparison with the previous results on the topic. By means of elementary methods, the author derives upper and lower bounds on the number of possible central configurations.