$(x_{0},y_{0})\in \mathcal{D}$ (including that one we want to control, i.e. the reference trajectory (RT)) is integrated;

3.  \[itm:T\] a specific integration time, $T,$ is set as long as the ensemble is followed. Hence, we can store the $x_0$ and $y_0$ initial positions of the trajectories, associated with given $v_{x0}$ and $v_{y0},$ surviving until $T.$ See example Fig. \[fig:rtbpl5\] – this procedure serves a well-defined ICM;

4.  \[itm:SM\] we follow the dynamics of the particles until the velocity of the RT fulfils the condition $v_x=0,\;v_y<0$ then repeat step \[itm:T\], i.e. we start the ensemble again from $\mathcal{D}$ but with the updated initial velocities ($0,v_{y}$).

Step \[itm:SM\] provides a series of the ICMs for those trajectories which start from domain $\mathcal{D}$ (Fig. \[fig:coosys\]) with velocity $(v_x=0,\;v_y<0).$ The points drawing these maps correspond to the stable manifold of the chaotic saddle in the $x-y$ section of the phase space. In other words, trajectories on these ICMs do not escape the system sooner than the integration time $T.$

From another point of view, in Hamiltonian systems with escape, one can consider that the system has an attractor at infinity. This means, there is a set of points on the ICMs whose end state is 