I moti quasi periodici e la stabilita' del sistema solare. II: Dai tori di Kolmogorov alla stabilita' esponenziale

This is the second part of a note devoted to the problem of stability of the solar system. The development of our knowledge in the last 50 years is considered, starting with the announcement of Kolmogorov's theorem on persistence of quasi periodic motions in 1954. The problem of applicability of the theorem to the planetary motions is discussed taking also into account the wide numerical explorations of the dynamics over billions of years performed during the last decades. It is shown that the picture drawn by collecting these results leads to the conclusion that chaos plays a non negligible role in the dynamical evolution of the solar system. A possible reconciliation between ordered quasi periodic motions and chaotic behaviour due to resonances might be offered by the theory of exponential stability which is illustrated in the final part of the note.