De Haerdtl inequality: an inequality of great dynamical interest in the Galilean system

The quasi-commensurability 7:3 between the mean motions of the Galilean satellites Ganymede and Callisto, known as De Haerdtl inequality, has never been taken into account in the scenarii of dynamical evolution of the Galilean satellites. We used numerical tools like frequency maps to detect the chaos induced by the inequality. We showed that it induces chaos, more particularly because of Callisto's eccentricity. Anyway, even if the orbits were nearly circular, Callisto's inclination is strong enough to induce chaos. This inclination is forced by the Sun, this means that Jupiter's obliquity is partly responsible of the chaos induced by De Haerdtl inequality. This chaos is due to Chirikov diffusion, say to overlaps of resonances.