Chaotic worlds: from order to disorder in gravitational N-body dynamical systems : [proceedings of the NATO Advanced Study Institute on Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems, Cortina, Italy, 8-20 September 2003

The gravitational N-body problem dominates much of theoretical astrophysics. It arises in problems ranging from the motion of artificial and natural satellites to the behaviour of stars in star clusters and galaxies. In the past, research in Celestial Mechanics has focused on analytical and numerical studies of ordered systems, with chaotic behaviour or disorder being the fascinating anomaly. Recently, however, scientists have begun to forge the link between order and disorder: designing new methods to recognise chaos’ signature and developing new theories on the sources of chaotic behaviour. They are applying these techniques successfully to solve real-world problems in solar system dynamics, galactic dynamics and other areas of physics such as particle acceleration. 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. Front Matter....Pages i-xi Canonical perturbation theory for nearly integrable systems....Pages 1-41 Periodic orbits in gravitational systems....Pages 43-79 Periodic solutions in Gravitational Problems and the Structure of Solution Space....Pages 81-101 General properties of three-body systems with Hill-type stability....Pages 103-128 Front Matter....Pages 130-130 The fine structure of Hamiltonian systems revealed using the Fast Lyapunov Indicator....Pages 131-165 Fourier analysis of chaotic motions and applications to Celestial mechanics....Pages 167-200 Front Matter....Pages 202-202 Basics of regularization theory....Pages 203-230 Order and chaos in Satellite encounters....Pages 231-251 Front Matter....Pages 254-254 Regular motions in extra-solar planetary systems....Pages 255-288 Tides on Europa....Pages 289-305 Numerical evaluation of Love's solution for Tidal amplitude....Pages 307-323 On the general solutions of Hilbert-Einstein field equations in vacuum....Pages 325-332 Back Matter....Pages 333-342 Based on the NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this textbook provides a reference volume for the students and researchers in gravitational n-body systems Edited By B.a. Steves, A.j. Maciejewski And M. Hendry. Proceedings Of The Nato Advanced Study Institute On 'chaotic Worlds...', Cortina, Italy, 8-20 September 2003--t.p. Verso. Includes Bibliographical References And Index.