Impact of Modern Dynamics in Astronomy : Proceedings of the IAU Colloquium 172 Held in Namur (Belgium), 6–11 July 1998

Modem dynamics is increasingly participating in the solution of problems raised by as­ tronomical observations. This new relationship is being fostered on one side by the im­ provements in the observations, which in recent years contributed several discoveries of new systems, such as the objects in the Kuiper belt, the pulsar and star companions, to speak only of the most striking ones, and, on the other hand, by the progresses in modem dynamics. The progresses in modem dynamics are due to two factors: the dissemination of fast computers, allowing the numerical studies of very complex systems by a large number of scientists, and the improvement in our understanding of the complex behaviour of Hamiltonian systems. KAM and Nekhorochev theories have shed a light on the subtle and surprizing interplays between regular and chaotic motions; numerical experiments and analytical approximations have shown how these peculiarities are indeed present in astronomically important systems and are instrumental in understanding their formation and evolution. Front Matter....Pages i-x Chaos in Relativity and Cosmology....Pages 1-16 Bianchi Cosmologies as Dynamical Systems....Pages 17-24 Slow and Fast Diffusion in Asteroid-Belt Resonances: A Review....Pages 25-37 Origin and Evolution of Near Earth Asteroids....Pages 39-50 Small Bodies in the Outer Solar System....Pages 51-54 The Use of Geocentric Variables to Search for Meteoroid Streams and Their Parents....Pages 55-64 A Symplectic Mapping Model as a Tool to Understand the Dynamics of 2/1 Resonant Asteroid Motion....Pages 65-76 On Stable Chaos in the Asteroid Belt....Pages 77-86 Explicit Semianalytical Theory of Asteroid Motion....Pages 87-96 On the Motion of Trapped Particles in the Vicinity of Corotation Centers....Pages 97-105 Migration of Trans-Neptunian Objects to the Earth....Pages 107-116 Trojans in Stable Chaotic Motion....Pages 117-126 Star Cluster Simulations: The State of the Art....Pages 127-137 Dimensionality of Stable and Unstable Directions in the Gravitational N -Boby Problem....Pages 139-147 Distribution of Kolmogorov-Sinaï Entropy in Self-Consistent Models of Barred Galaxies....Pages 149-158 Regular and Chaotic Motion in Globular Clusters....Pages 159-168 Periodic Orbits Around a Massive Straight Segment....Pages 169-178 Escape from a Crisis in Fokker-Planck Models....Pages 179-186 Building Galaxy Models with Schwarzschild Method and Spectral Dynamics....Pages 187-194 Conditional Entropy....Pages 195-209 Detection of Ordered and Chaotic Motion Using the Dynamical Spectra....Pages 211-220 Cantori, Islands and Asymptotic Curves in the Stickiness Region....Pages 221-230 Parallel/Vector Integration Methods for Dynamical Astronomy....Pages 231-241 Do Average Hamiltonians Exist?....Pages 243-248 Diffusion Character in Four-Dimensional Volume-Preserving Map....Pages 249-258 The Separatrix Algorithmic Map: Application to the Spin-Orbit Motion....Pages 259-268 Canonical Variables of the Second Kind and the Reduction of the N-Body Problem....Pages 269-280 Motion Near the Unit Circle in the Three-Body Problem....Pages 281-290 A Global Analysis of the Generalized Sitnikov Problem....Pages 291-302 The Hamiltonian Dynamics of the Two Gyrostats Problem....Pages 303-312 Planetary Systems....Pages 313-316 Complements to Moons’ Lunar Libration Theory....Pages 317-328 Impact of the Quadrupole Moment of the Sun on the Dynamics of the Earth-Moon System....Pages 329-338 The Effect of C 22 on Orbit Energy and Angular Momentum....Pages 339-348 The Use of Lie Series in the Construction of A Perturbation Theory and Some Recent Results in the Theory of the Motion of Hyperion....Pages 349-358 Higher Order and Iterative Theories to Compute Asteroid Mean Elements....Pages 359-360 The Asteroid Mass Determination Project at the U.S. Naval Observatory....Pages 361-362 The Asteroid Identification Problem....Pages 363-364 Interaction of Resonances and Yarkovsky Non-Gravitational Effects in the Asteroid Belt....Pages 365-368 Target Plane Confidence Boundaries: Mathematics of the 1997 XF11 Scare....Pages 369-370 A Dynamical Survey of Inner Solar System Asteroids....Pages 371-372 Detailled Study of the Dynamics of Fragments of Comet C/1996 B2 Hyakutake....Pages 373-374 Proper Elements and Stability of the Trojan Asteroids....Pages 375-376 Dynamical Behaviour of Asteroids in the 4:1 Resonance....Pages 377-378 Perturbations of Small Moons Orbits Due to Their Rotation: The Model Problem....Pages 379-380 Mean Motion Resonances in the Asteroid Belt....Pages 381-382 On the Critical Phenomena in the Dynamics of Asteroids....Pages 383-386 Dynamics of Real Asteroid at the Hecuba Gap....Pages 387-388 Modelling Very-High-Eccentricity Asteroidal Librations with the Andoyer Hamiltonian....Pages 389-390 Resonant Relaxation....Pages 391-392 Periodic Orbits in Three-Armed Galaxies....Pages 393-394 Orbits in a Stäckel Approximation....Pages 395-396 Measuring Mass Loss Rates from Galactic Satellites....Pages 397-398 Effect of Chaotic Orbits on Dynamical Friction....Pages 399-400 Nonparametric Statistical Models of Globular Cluster Dynamics....Pages 401-402 Orbits of Hepparcos Metal-Poor Stars with Well-Defined Spectroscopic Abundances....Pages 403-404 HST-FGS Astrometry of the Low Mass Binary L722-22....Pages 405-407 Can Combination of ‘Kozai Effect’ and Tidal Friction Produce Close Stellar and Planetary Orbits?....Pages 409-410 Simple Periodic Orbits in Elliptical Galaxies Modelled by Hamiltonians in 1-1-1 Resonance....Pages 411-412 Moon’s Planetary Perturbations....Pages 413-414 On Construction of a Long-Term Moon’s Theory....Pages 415-416 A New Model of Mars Rotation from Pathfinder Data....Pages 417-418 Dynamics of the Mimas-Tethys System....Pages 419-424 A Necessary Condition to the Simultaneous Correction of Celestial Reference Frames and Minor Planets Orbital Elements....Pages 425-426 Secular Perturbations Near Mean Motion Resonances....Pages 427-428 Dynamics of Fictitious Earth’s Satellites with Possible Past Values of the Ecliptic....Pages 429-430 An Intermediary Periodic Orbit for Hyperion....Pages 431-432 Averaging of Earth-Crossing Orbits....Pages 433-434 Rotational Motion of Celestial Bodies in the Relativistic Framework....Pages 435-436 Lommel Functions in Some Drag-Perturbed Problems....Pages 437-438 Two Conjectures of G.D. Birkhoff....Pages 439-440 Three-Body Stability Criteria....Pages 441-442 Nekhoroshev Stability in Quasi-Integrable Degenerate Hamiltonian Systems....Pages 443-444 Nekhoroshev-Stability of L 4 and L 5 in the Spatial Restricted Problem....Pages 445-446 Effective Lyapunov Numbers and Correlation Dimensions in a 3-D Hamiltonian System....Pages 447-448 A Symplectic Integration Scheme that Allows Close Encounters Between Massive Bodies....Pages 449-450 Analytical Approximation of the Dissipative Standard Map....Pages 451-452 Second Order Perturbations of Elliptic Elements with Respect to the Initial Ones....Pages 453-454 Zonal Harmonics of the Gravity Field in DEF-Variables....Pages 455-456 On the Stability of Stationary Solutions of the Twice-Averaged Hill’s Problem Taking into Account the Planet Oblateness....Pages 457-457 Study of the Normal Variational Equation in an Homogeneous Field of Degree Five....Pages 459-460 Generalized Gylden-Type Systems in Universal DS-Like TR-Variables....Pages 461-462 Orbital Structure of the Two Fixed Centres Problem....Pages 463-464 Chaos in Three-Body Dynamics: Intermittency, Strange Attractor, Kolmogorov-Sinai Entropy....Pages 465-466 This volume of proceedings contains review and research papers concerning the impact of modern dynamics in astronomy. Modern dynamics is playing an increasing role in the solution of problems raised by astronomical observations. This new relationship is being fostered by recent discoveries of new systems, such as the Kuiper belt, pulsar and star companions; by progress in theoretical dynamics, like KAM and Nekhorochev theories and adiabatic invariants; and by the dissemination of fast computers. The two main areas of applications which are discussed are `stellar systems', including dynamics of galaxies, and `small bodies in the solar system'. In both cases the concepts and tools of chaotic motion are considered and fully discussed. This book is an up-to-date source of information for astronomers interested in the dynamics of the solar system or of stellar systems, as well as for dynamicists who wish to understand the impact of modern theories of chaos in astronomy.