projection of all the rest components of the positions and velocities. In contrast, the above defined ICMs are suitable to visualize the escape dynamics even on Poincaré surfaces of sections. This means, the initial conditions in general belong to a well-defined configuration of the system, i.e. Moon’s and Sun’s positions and all the velocities are fixed. Therefore, the escape dynamics are fully characterized by the initial coordinates and velocities of the test particle for a given energy level. Using a statistical approach by means of an ensemble, the initial positions in $x-y$ configuration plane depict the filamentary fractal set corresponding to the finite time chaotic motion before escape. This object can be thought as of the intersection of the $x-y$ plane and the stable manifold of a higher dimensional chaotic saddle. Therefore, we want to use the ICMs to apply the control to the spacecraft’s motion.

Interestingly, however, one might also find regular structures in the configuration space. Very long calculations represent that there are trajectories that form a torus in the $x-y$ plane, see Fig. \[fig:KAM\_torus\]. These points represent test particles orbiting the Earth at $t=5\cdot 10^5$ days, panel (b), and $t=10^6$ days panel (c), respectively. Higher dimensional ($D>2$) 