Long-term evolution of the GJ 163 planetary system over 1 Gyr starting with the orbital solution from Table 2. We did not include tidal effects in this simulation. The panel shows a face-on view of the system invariant plane. x and y are spatial coordinates in a frame centered on the star. Present orbital solutions are traced with solid lines and each dot corresponds to the position of the planet every 0.1 Myr. The semi-major axes are almost constant, and the eccentricities present slight variations (0.061 < e_b < 0.101, 0.067 < e_c < 0.109, and 0.372 < e_d < 0.374).