Analysis of the distribution of times of escape in the N-body ring problem

Abstract

This paper summarizes the results of a numerical investigation of the phenomenon of escape in the N-body ring problem. There is a 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 for N = 5, 6, 7, 8. We have also analyzed the percentage of escaping orbits, the direction of escape and the distribution of the times of escape.