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

Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.

The only textbook giving an up-to-date review of the latest methods of analysis for understanding ordered and chaotic behaviour in gravitational n-body systems and their application to real motion in planetary systems The reviews are written by internationally renowned scientists working at the forefront of their field One of only a few recent textbooks written for PhD level researchers in n-body dynamical systems Provides a comprehensive review from the fundamental mathematics underpinning modern studies of ordered and chaotic behaviour in n-body dynamics to the latest developments and applications

Inhalt
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.