Topics in Gravitational Dynamics

An Overview on the Nekhoroshev Theorem.- Diffusion in Hamiltonian Quasi-Integrable Systems.- Weakly Dissipative Systems in Celestial Mechanics.- Connectance and Stability of Dynamical Systems.- Chaotic Di?usion of Asteroids.- An Overview of the Rotations of Planets in the Solar System.- On the Stability of Extra-Solar Planetary Systems.- Origin Theories for the Eccentricities of Extrasolar Planets.- Methods for the Study of the Dynamics of the Oort Cloud Comets I: Modelling the Stellar Perturbations.- Methods for the Study of the Dynamics of the Oort Cloud Comets II: Modelling the Galactic Tide.- Special Features of Galactic Dynamics.- On the Diffculty to Foresee Solar Cycles: A Non-Deterministic Approach.

This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. Emphasis is on questions of stability of planetary systems. In particular the discovery and thus the possibility to study many new extra-solar planetary systems have spurred new developments in the field and enabled the testing and enlargement of the domains of validity of theoretical predictions through the Nekhoroshev theorem.