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. Glska (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.

Inhalt
Stability Theory in Celestial Mechanics.- Modern Dynamical Systems Theory.- The Present State of the n-Body Problem.- Bode's Law.- Distribution of the Mean Motions of Planets and Satellites and the Development of the Solar System.- Can the Solar System be Quantized?.- On the Original Distribution of the Asteroids.- The Origin of Commensurabilities in the Satellite Systems.- The Origin of the Asteroid Ring.- Orbits of Trojan Asteroids.- The Role of Saturn's Oblateness in the Mimas-Tethys Resonance.- Stability of Asteroidal Motion in the Hecuba Gap.- Secular Perturbations for Asteroids Belonging to Families.- The Formation of Disks by Inelastic Collisions of Gravitating Particles. Applications to the Dynamics of the Saturn's Ring and to the Formation of the Solar System.- Stationary Solutions of the Averaged Three-Body Problem and Some Problems of Planet Motion Stability.- Integrable Cases of Satellite Problem with the Third Body and the Oblate Planet.- The Global Solution in the Problem of the Critical Inclination.- Retrograde Satellites in the Circular Plane Restricted Three-Body Problem.- A Note on a Separation of Equations of Variation of the Elliptic Restricted Three-Body Problem into Hill's Equations.- Comet Schwassmann-Wachmann 3 (1930 VI).- The Motion of Comet Westphal in 18521974.- The Motion of Comet Encke-Backlund over 19011970.- An Iterative Method of General Planetary Theory.- On the Calculation of Secular Perturbations in the Case of Close Commensurability.- Long Period Terms in the Solar System.- On the Theory of the Galilean Satellites of Jupiter.- Conditions for Escape and Retention.- Influence of the Dynamical Figure of the Moon on Its Rotational-Translational Motion.- A Comparison of the Mean-Value and Initial-Value Solutions of the IdealResonance Problem with an Application in Rigid-Body Mechanics.- Statistics of Three-Body Experiments.- The Role of Binaries in Cluster Dynamics.- On the Stability of Small Clusters or Cluster Remnants.- The Dynamical Evolution of Trapezium Systems.- The Stability of Triple Stellar Systems.- Sur un invariant intégral du problème des n corps: Conséquence de l'homogénéité du potential.- Numerical Experiments on Expanding Gravitational Systems.- Numerical Experiments on the Stability of Spherical Stellar Systems.- On the 'Thermodynamics' of Self-Gravitating N-Body Systems.- Dynamics and Clusters of Galaxies.- Dynamical Friction Effects on the Motion of Stars in Rotating Spherical Clusters.- On the Disappearance of Isolating Integrals in Dynamical Systems with More than Two Degrees of Freedom.