New Developments in the Dynamics of Planetary Systems : Proceedings of the Fifth Alexander Von Humboldt Colloquium on Celestial Mechanics Held in Badhofgastein (Austria), 19–25 March 2000

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 in the Austrian Alps at the invitation of R. Dvorak. This time the colloquium was held at Badhofgastein from March 19 to March 25, 2000 and was devoted to the 'New Developments in the Dynamics of Planetary Systems'. The papers covered a large range of questions of current interest: t- oretical questions (resonances, KAM theory, transport, ... ) and questions about numerical tools (synthetic elements, indicators of chaos, ... ) were particularly well represented; of course planetary theories and Near Earth Objects were also quite popular. Three special lectures were delivered in honor of deceased colleagues whom, to our dismay, we will no longer meet at the 'Austrian Colloquia'. W. Jefferys delivered the Heinrich Eichhorn lecture on 'Statistics for the Twenty-first Century Astrometry', a topic on which Heinrich Eichhorn was a specialist. A. Roy delivered a lecture honoring Victor Szehebely on 'Lifting the Darkness: Science in the Third Millenium', in which in wove anecdotes and remembrances of Victor which moved the audience very much. A. Lemaitre spoke in honor of Michele Moons on 'Mech­ anism of Capture in External Resonance'. The end of her talk was devoted to a short and moving biography of Michele illustrated by many slides. Front Matter....Pages i-1 Statistics for Twenty-First Century Astrometry....Pages 3-16 Synthetic Proper Elements for Outer Main Belt Asteroids....Pages 17-46 Invariant Tori in the Secular Motions of the Three-Body Planetary Systems....Pages 47-74 Improvements of Planetary Theories over 6000 Years....Pages 75-82 The Distribution of Energy Perturbations at Planetary Close Encounters....Pages 83-91 Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for Their Origins....Pages 93-112 The Phase Space Structure Around L 4 in the Restricted Three-Body Problem....Pages 113-123 Why do Trojan ASCs (Not) Escape?....Pages 125-136 The 2/1 and 3/2 Resonant Asteroid Motion: A Symplectic Mapping Approach....Pages 137-150 Twist and Non-Twist Bifurcations in a System of Coupled Oscillators....Pages 151-160 The Mel’nikov Subharmonic Function and the Non-Existence of Analytic Integrals in Non-Autonomous Systems....Pages 161-166 On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: A Very Sensitive Tool....Pages 167-195 Crossing of Various Cantori....Pages 197-210 Fractal Dimensions as Chaos Indicators....Pages 211-225 Normal Form Invariants Around Spin-Orbit Periodic Orbits....Pages 227-241 The Third Integral in a Self-Consistent Galactic Model....Pages 243-263 Counterrotating Galaxies and Memory of Cosmological Initial Conditions....Pages 265-278 The Family P 12 of the Three-Body Problem — the Simplest Family of Periodic Orbits, with Twelve Symmetries per Period....Pages 279-298 The Caledonian Symmetrical Double Binary Four-Body Problem I: Surfaces of Zero-Velocity Using the Energy Integral....Pages 299-318 Application of the Nonrestricted Three-Bodies Problem to the Stellar System ξ UMa....Pages 319-324 Periodic Solutions of the Planetary 5:2 Resonance Three-Body Problem....Pages 325-328 Limits of Stability for Planets in Double Star Systems Using the Fast Lyapunov Indicators....Pages 329-335 On a Fokker-Planck Approach to Asteroidal Transport....Pages 337-340 Fractality in a Galactic Model....Pages 341-347 Transformation Methods for Trigonometric Parallaxes....Pages 349-359 The Search for Exosolar Systems....Pages 361-362 The Two Fixed Centers Problem Revisited....Pages 363-366 The Phase Space Structure of the General Sitnikov Problem....Pages 367-379

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 topics; symplectic method of numerical integration of Hamiltonian systems and methods for special analysis of computed orbits leading to refined tools for the detection and evaluation of chaos.
The dynamics of the asteroid belt and of NEOs (near Earth objects), two important topics with implications on the evolution of planetary systems and on the assessment of probabilities of catastrophic collisions, are also covered.
This volume will be of interest to mathematicians and physicists interested in Hamiltonian mechanics and in the dynamics of planetary systems.

Proceedings of the 5th Alexander von Humboldt Colloquium on Celestial Mechanics