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.
The aim of this paper is to analyze the effect of the mass ratio on the distribution of short times of escape and the probability of escape of a particle from the 4-body ring configuration. To this purpose, we carry out a numerical exploration of the problem, considering three different values of the mass ratio between the central and the primary bodies and, for each of these values, a pair of values of the Jacobi constant.
In this work, we perform a numerical exploration of the escape in the N-body ring problem in absence of a central body, for $$4\le N\le 9$$
4
≤
N
≤
9
and ten values of the Jacobi constant. We show how the probability of escape per interval of time varies as a function of the Jacobi constant, finding that, for values of the Jacobi constant smaller than a certain limit value, the probability of escape from the system tends to decrease with time. However, if we consider values of the Jacobi constant larger than this limit value, the probability of escape grows with time, for times of escape smaller than 100 units of time.
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