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.

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.

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Context. The current IAU2000 nutation model performed different approximations, one of them being that the Oppolzer terms associated to the planetary perturbations of the nutations were assumed to be smaller than 5 μas and thus were neglected. At present, the uncertainties of the amplitudes of individual components of the observed nutations are better, and the conventional nutation model does not fit the accuracy requirements pursued by the International Astronomical Union (IAU) and the International Association of Geodesy (IAG). Aims. The objective of this work is to estimate the magnitude of the lacking Oppolzer terms of the planetary nutations and find out whether they are still negligible or not. Methods. The Oppolzer terms resulting from the direct and indirect planetary perturbations of the Earth’s rotation have been computed for a two-layer Earth model following the Hamiltonian theory of the non-rigid-Earth. Results. The planetary Oppolzer terms for the non-rigid Earth are not really negligible as believed, and some of them have amplitudes larger than 10 μas, therefore significantly above the current level of uncertainty of individual harmonic constituents. Conclusions. In the short term, the IAU2000 nutation model must be supplemented with suitable corrections accounting for those missing components; its planetary component must be thoroughly revised in the medium term.

The aim of this paper is to start a numerical exploration of the escape in thebody ring problem. When the energy of the orbits is larger than the escape energy, test particles may escape through any of the openings of the potential well. We have computed the "basins" of escape towards the different directions by means of Poincaré sections. We have also analyzed the proportion of escaping orbits and the direction of escape.