Topics in Gravitational Dynamics
This book is the outcome of the 2006 Aussois Winter School: “Open problems inCelestialMechanics”.Inthis school,wehavereviewedthe stateof theartin the theory and applications of dynamical systems with particular interest in planetary and galactic dynamics. Recent developments have been achieved in two directions: (1) the application of Nekhoroshev’s theorem to the motion of planets and asteroids and (2) the dynamical origin of the diversity of the extra-solar planetary systems. The aims of the 2006 Aussois Winter School and consequently those of this book are: • To provide a review of the dynamics of quasi-integrable Hamiltonian s- tems from the viewpoint of Nekhoroshev’s theorem and its implications for slow di?usion processes. • To introduce the dynamics of weakly dissipative systems. • To review the dynamics of small bodies in the solar system. • To discuss the dynamical origin and the diversity of the extra-solar pl- etary systems. • To highlight special problems in galactic dynamics. Acknowledgments The editors thank with great pleasure the sponsorship of the O.C.A. (- servatoire de la Côte d’Azur) and of the Département Cassiopée, together with the CNRS (the french “Centre National de la Recherche Scienti?que”), throughitsContinuingEducationDepartment(“FormationPermanente”)and its sta?, with a special mention to Mrs Jocelyne Gosselin. U.N.S.A./C.N.R.S./O.C.A. Observatoire de Nice, Daniel Benest February 2007 Claude Froeschlé Elena Lega VI Preface Bibliography 1. Benest,D.andFroeschlé,C.(eds),1990.LesméthodesmodernesdelaMécanique Céleste [Modern Methods of Celestial Mechanics], Editions Frontieres (C36).