The Stability of the Solar System and of Small Stellar Systems

The IAU Symposium No. 62, 'The Stability of the Solar System and of Small Stellar Systems' was held in Warsaw in Poland during the Extraordinary General Assembly of the IAU in commemoration of the SOOth anniversary of the birth of Nicolaus Copernicus. The Symposium was sponsored by Commission 7 (Celestial Mechanics) and cosponsored by Commissions 4 (Ephemerides) and 37 (Star Clusters and Asso- ciations) of the IAU and by IUTAM. The Organizing Committee included Y. Kozai (Chairman), J. A. Agekjan, A. Deprit, G. N. Duboshin, S. G\lska (Local represen- tative), M. Henon, B. Morando and C. Parkes (IUTAM representative). The Symposium was supported financially by the IA U, the IUT AM and the Polish Academy of Sciences. Y. KOZAI Chairman of the Organizing Committee STABILITY THEORY IN CELESTIAL MECHANICS J MOSER Courant Institute of Mathematical ScIences, New York University, New York, N. Y. 10012, U.S.A. Abstract, This expository lecture surveys recent progress of the stability theory in Celestial Mechanics with emphasis on the analytical problems. In particular, the old question of convergence of perturbation series are discussed and positive results obtained, in the light of the work by Kolmogorov Arnold and Moser. For the three body problem, classes of quasi-periodic solutions and doubly asymptotic (or homo- clinic) orbits are discussed.