Stability and Chaos in the Solar System: From Poincaré to the present

Abstract: Some of the most famous works of Henri Poincaré (1854-1912) have been motivated by the problem of the stability of the Solar System. Indeed, since its formulation by Newton, this problem has fascinated astronomers and mathematicians, searching to prove the stability of the Solar System. Poincaré demonstrated that the perturbative methods of the astronomers could not be used to provide an answer to the problem of stability on infinite time because the series that were used are in general divergent. At the same time he believed that the dissipative terms would be of larger importance than the conservative neglected terms, leading to a stable final state for the Solar System. In the following of the work of Poincaré, KAM theorems have provided new hopes for mathematicians to prove the stability of the Solar System. On the opposite, the recent numerical works on realistic models of the Solar System show that the system is unstable in the strong sense and that planetary collisions are possible within the lifetime of the Sun.