Synopses & Reviews
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.
Synopsis
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."
Table of Contents
Preface;
R. Dvorak, J. Henrard. Heinrich K. Eichhorn memorial lecture, Statistics for Twenty-first Century Astrometry;
W.J. Jefferys. Asteroid Synthetic Proper Elements;
Z. Knezevic, A. Milani. Invariant Tori in the Secular Motions of the Three-Body Planetary Systems;
U. Locatelli, A. Giorgilli. The Improvements of Planetary Theories over 6000 Years;
J. Chapront. The Distribution of Energy Perturbations at Planetary Close Encounters;
G.B. Valsecchi, et al. Dynamics of Small Earth-Approachers on low-eccentricity Orbits and Implication for their Origin;
P. Michel, Ch. Froeschlé. The Phase Space Structure around
L_{4} in the Restricted Three-Body Problem;
Z. Sándor, et al. Why do Trojan ASCs (not) escape?
R. Dvorak, K. Tsiganis. The 2/1 and 3/2 Resonant Asteroid Motion: a Symplectic Mapping Approach;
J. Hadjidemetriou, G. Voyatzis. Twist and non-twist bifurcations in a system of coupled oscillators;
G. Stagika, S. Ichyiaroglou. The Mel'nikov Subharmonic Function and the Non-existence of Analytic Integrals in Non-autonomous Systems;
E. Meletlidou. On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: a very Sensitive Tool;
C. Froeschlé, E. Lega. Crossing of Various Cantori;
G. Contopoulos, et al. Fractal Dimensions as Chaos Indicators in the Standardmap;
F. Freistetter. Normal Form Invariants around Spin-Orbit Periodic Orbits;
A. Celletti, C. Falcolini. The Third Integral in a Self-Consistent Galactic Model;
G. Contopoulos, et al. Counter-rotating Galaxies and Memory of Cosmological Initial Conditions;
N. Voglis, et al. The Family
P_{12} of the Three-Body Problem: the Simplest Family of Periodic Orbits with Twelve Symmetries per Period;
C. Marchal. Surfaces of Separation in the Symmetrical, Coplanar, Equal Mass, Four Body, Double Binary Problem;
B. Steves, A. Roy. About One Case of the Non-Restricted Three Body Problem;
N.A. Solovaya, E.M. Pittich. Periodic solutions of the planetary 5:2 resonance three-body problem;
T. Michtchenko, S. Ferraz-Mello. Short Liapunov Indicators for Planets in Double Star Systems;
E. Pilat-Lohinger. On a Fokker-Planck Approach to Asteroidal Transport;
K. Tsiganis, et al. Fractal Windows for Escaping Stars;
J.F. Navarro, J. Henrard. Transformation Methods for Trigonometric Parallaxes;
H. Smith. The Search for Exosolar Systems;
P.K. Seidelmann. The Two Fixed Centers Problem Revisited;
H. Varvoglis, et al. The Phase Phase Structure of the General Sitnikov Problem;
J. Kallrath, R. Dvorak.