The Dynamical Behaviour of Our Planetary System : Proceedings of the Fourth Alexander Von Humboldt Colloquium on Celestial Mechanics

It is now a well established tradition that every four years, at the end of winter, a group of "celestial mechanicians" from all over the world gather at the "Alpen­ gasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was held from March 17 to March 23, 1996 and was devoted to the Dynamical Behaviour of our Planetary System. The papers covered a large range of questions of current interest: theoretical questions (re- nances, universal properties, non integrability, transport, ... ) and questions about numerical tools ( symplectic maps, indicators of chaos, ... ) were particularly well represented; the never ending problem of the sculpting of the asteroid belt was also qui te popular. You will find in the following pages a pot-pourri of what we listen to; you will miss of course the diversity of accents with which the tunes were delivered: from China, from Japan, from Brazil, from the United-States of America and from all over Europe, East and West. Let us not forget that the comet 199682 (Hyakutake) came to visit us; many an evening was spent on the deck of the Alpengasthof contemplating this celestial visitor who liked to play hide-and-seek behind the spruce trees. Front Matter....Pages i-ix Scattering By Resonances....Pages 1-20 Non-Integrability in Hamiltonian Mechanics....Pages 21-31 Regular and Irregular Periodic Orbits....Pages 33-56 Universal Properties of Escape in Dynamical Systems....Pages 57-68 Mapping and Dynamical Systems....Pages 69-84 A New Fast Fourier Method for Evaluating Fourier Spectra at Arbitrary Frequencies....Pages 85-94 On the use of Analytical Theories in the Calculation of Precession-Nutation....Pages 95-106 The Nekhoroshev Theorem and the Asteroid Belt Dynamical System....Pages 107-136 Frequency Modified Fourier Transform and its Application to Asteroids....Pages 137-148 The Trojan Problem....Pages 149-164 Dynamical Transport to Planet-Crossing Orbits....Pages 165-173 Review of the Dynamics in the Kirkwood Gaps....Pages 175-204 Open Problems on the Eve of the Next Millennium....Pages 205-211 Limits of Comprehension, Reference Frames and General Relativity....Pages 213-222 Stable Chaos: A First Model....Pages 223-231 Transport in Perturbed Integrable Hamiltonian Systems and the Fractality of Phase Space....Pages 233-242 Equilibria Bifurcations of Satellite Orbits....Pages 243-255 Fast Lyapunov Indicators Comparison with other Chaos Indicators Application to Two and Four Dimensional Maps....Pages 257-275 Asteroid Motion Near the 2:1 Resonance: A Symplectic Mapping Approach....Pages 277-290 Symplectic Integrators for Hill’s Lunar Problem....Pages 291-305 Rotation Number and Global Stability of Symplectic Integrator....Pages 307-319 On a Global Expansion of the Planar Disturbing Function....Pages 321-332 Links Between Time Scales Using Barycentric Relativistic Ephemerides....Pages 333-344 Orbital Stability of Planetary Quasi-Satellites....Pages 345-355 Alternative Derivations of Perturbations with Use of a Mixed Reference-Plane System: Application to the Motion of the Orbit Plane of Hyperion....Pages 357-363 Astrodynamic Study of the Earth Rotation....Pages 365-376 Orbital Evolution of Asteroids in the Hecuba Gap....Pages 377-384 A Study of the Local Lyapunov Numbers for Orbits in the Outer Solar System....Pages 385-392 On the Influence of Supernova Shockfronts on the Stability of the Solar System....Pages 393-401 Henri Poincaré: A Decisive Contribution to Special Relativity....Pages 403-413 Periodic Orbits in the Sitnikov Problem....Pages 415-428 The papers in this volume cover a large range of questions concerning the dynamics of objects of the Solar System, from theoretical Hamiltonian mechanics to the study of the dynamical behaviour of specific objects, with a strong emphasis on the detection, causes and effects of chaotic behaviour. Several papers describe the very latest contributions in two very lively and recent topics which are considered as a major breakthrough in numerical dynamics: symplectic methods of numerical integration of Hamiltonian systems, and methods for spectral analysis of numerically computed orbits leading to refined tools for the detection and evaluation of chaos. The dynamics of the asteroid belt and other small objects, a fast-moving topic with important implications for the origin and evolution of the Solar System, is also extensively covered. The volume will be of interest to mathematicians and physicists interested in Hamiltonian mechanics and in the dynamics of the Solar System.