Diagrams showing the dynamic of the selected groups. In all panels, the GE is shown in light green, the prograde halo group in blue, the retrograde group in light brown, and the most retrograde group in violet. Top left: Lindblad diagram (L_z × E_n). Top right: Toomre Diagram. Middle left: eccentricity as a function of the galactocentric distance (R_gal). Middle right: cylindrical velocity components, V_ϕ, as a function of the radial component, V_r. Bottom left: maximum distance from the Galactic (Z_max) plane as a function of eccentricity. The dashed line at Z_max = 2 kpc indicates the scale height of the thick disc (Li et al. 2018). Bottom right: radial action () as a function of the orbital angular momentum, L_Z.