Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.

Automated summary

In this paper, we numerically investigate particle escape in two different dynamical systems with the same number of exit channels. The study reveals a previously undetected sequential pattern in the distribution of escape times in the galactic system. It is demonstrated that this pattern is directly linked to the geometry of the stable manifolds to the Lyapunov orbits at the potential openings. Furthermore, the study shows that the different nature of the two systems affects the process of escape due to differences in the geometry of the manifolds to the Lyapunov orbits.