A FEW POINTS ON THE STABILITY OF THE SOLAR-SYSTEM

The secular equations which were used to exhibit the chaotic behaviour of the solar system (Laskar, 1989) are established here in a Hamiltonian framework. The integration cf the former secular equations over 400 Myr showed that the two resonant arguments 2(omega-4.BAR - omega-3.BAR) - (OMEGA-4. - OMEGA-3.) and (omega-1.BAR - omega-5.BAR) - (OMEGA-1. - OMEGA-2.) given in (Laskar, 1990) present both transitions from libration to circulation. During the circulation of the first argument, temporary libration of the argument (omega-4.BAR - omega-3.BAR) - (OMEGA-4. - OMEGA-3.) is observed, revealing resonance overlap beetween these two resonances, which explains the existence of a large chaotic zone for the motion of the solar system.