On the analysis of the fractal basins of escape in the N‐body ring problem

Abstract

This article summarizes the results of a numerical investigation of the phenomenon of escape in the N‐body ring configuration, focusing on the scenarios that result for N = 5, 6, 7, 8 peripheral bodies. There is a critical value of the Jacobi constant of the system such that for smaller values, the potential well opens and test particles may leave the potential through any of its N openings. By means of a surface of section, we show the results of the computation of the basins of escape towards the different directions of escape, analyzing the structures that appear in them.