to that what we have seen in Fig. \[fig:velocity\]. Fig. \[fig:no\_control\] (a) shows the ICM containing $3.6\cdot10^5$ test particles starting from the region $x_0\in[-1.15,-0.7],\;y_0\in[-0.4,0.3]$ with the velocity of the $L_5$ Lagrangian point. The RT is selected in such a way that $(x_0,y_0)=(-0.914,0.068)$ and $(v_{x_0},
v_{y_0})=(-0.02527,-0.22865),$ see Table \[table:epoch\] third column. These initial conditions correspond to the $L_5$ point in RTBP. Test integrations show that the RT leaves the system at around 500 days. Therefore, the task is to keep this trajectory in the system for an arbitrary long period of time ($t\gg\tau$). The ICM is constructed as usual, where black dots represent the trajectories not leaving the system until $T$=400 days, and the red cross shows the RT on the map.

![image](fig6a){width="55mm"} ![image](fig6b){width="55mm"} ![image](fig6c){width="55mm"}\
![image](fig6d){width="55mm"} ![image](fig6e){width="55mm"} ![image](fig6f){width="55mm"}\

The next step is to follow the RT until the criterion $v_x=0 , v_y<0$ is fulfilled. Then we check the actual $v_y=-0.229$ of the RT, and depict a new ICM again for $T$=400 days, with these velocities ($v_{x0}=0 , v_{y0}=-0.229$) as updated initial velocities, see Fig \[fig:no\_control\] (b).

Since the initial velocity $v_{x_0}$ of the $L_5$ point is very close to zero, we do not have to wait too long for the second 