controls can be applied to transfer the trajectory to the other (desirable) basin. Consequently, small perturbations lead to success, which are more likely in cases when the basin boundaries are fractal sets (box counting dimension $D<1$), which is particularly common in high dimensional chaotic systems.

In what follows, we describe how to use the above mentioned methods to the RFBP. Although there are many parameters (masses, eccentricities of primaries) in a real situation we are not able to vary any of them. Therefore, we might want to adjust the velocity of the test particle in order to control its phase space position. This can be done by using a tangential force continuous in time. Initial condition maps can be suitable representations of the dynamics that tell us how to apply the control force. A brief description of the intervention procedure is given as follows:

1.  \[itm:r\] a pre-defined region which we are interested in as a possible domain of controlled motion, $r<1.5$ is chosen around the Earth (Figure \[fig:coosys\]). If the trajectory leaves this part of the configuration space, it is recorded as an escaped trajectory;

2.  \[itm:N0\] the motion of large number of particles originating around the $L_5$ point 