Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems

Tools of Order.- Canonical perturbation theory for nearly integrable systems.- Periodic orbits in gravitational systems.- Periodic solutions in Gravitational Problems and the Structure of Solution Space.- General properties of three-body systems with Hill-type stability.- Tools for investigation of Chaos and its sources.- The fine structure of Hamiltonian systems revealed using the Fast Lyapunov Indicator.- Fourier analysis of chaotic motions and applications to Celestial mechanics.- Sources of Chaos.- Basics of regularization theory.- Order and chaos in Satellite encounters.- Applications.- Regular motions in extra-solar planetary systems.- Tides on Europa.- Numerical evaluation of Love's solution for Tidal amplitude.- On the general solutions of Hilbert-Einstein field equations in vacuum.