On the use of surfaces of section in the N‐body ring problem

Abstract

In the N‐body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N‐body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.