Singularities in Gravitational Systems: Applications to Chaotic Transport in the Solar System

Alessandra Celletti (auth.), Daniel Benest, Claude Froeschlé (eds.)3540437657, 9783540437659

Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.

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Table of contents :
Singularities, Collisions and Regularization Theory….Pages 1-24
The Levi-Civita, KS and Radial-Inversion Regularizing Transformations….Pages 25-48
The Birkhoff and B 3 Regularizing Transformations….Pages 49-62
Perturbative Methods in Regularization Theory….Pages 63-71
Collisions and Singularities in the n -body Problem….Pages 72-80
Triple Collision and Close Triple Encounters….Pages 81-100
Dynamical and Kinetic Aspects of Collisions….Pages 101-113
Chaotic Scattering in Planetary Rings….Pages 114-144
Close Encounters in Öpik’s Theory….Pages 145-178
Generalized Averaging Principle and Proper Elements for NEAs….Pages 179-211