Jacques Henrard - Böcker

Proceedings of the Alexander von Humboldt Colloquium on Celestial Mechanics held in Ramsau, Austria, March 13-19, 1988

This volume contains the papers presented at the Third Alexander von Humboldt Colloquium on Celestial Mechanics. The papers cover a large range of questions, from the behaviour of dust particles to the stability of the solar system as a whole. The motions of asteroids and their classification into families are also discussed. Specific topics addressed are KAM theory, chaotic motions, resonances, Lyapunov characteristic exponents, perturbation theory and numerical integration.

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 contributions in two 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.

This volume of proceedings contains research and review papers concerning the dynamics of asteroids and comets and especially their interactions with the Earth as signified by geological and historical records. Remembering what may have happened to the dinosaurs, but being careful to avoid creating irrational scares, the papers attempt to improve our knowledge of dynamics of the small objects of the Solar System and to assess in particular their effects on the Earth environment and the evolution of life.

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 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.

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 contemporary 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.

This book is intended to diffuse original research results interesting people working in Celestial Mechanics in both theory and applications. Theoretical investigators will find several results on Hamiltonian Dynamics, periodic Orbits, Chaos Diagnostic and Perturbations Theory. Applications cover several directions of research starting with those related to space exploration (mission design and space research) to those related to astronomy (extrasolar planets, asteroids, Near Earth asteroids). Since this book carries original results, it is unique and complements similar books and journals. Some of the subjects have great media appeal: the risk of impact of space debris on the Space Station, the possibility of fly-by missions to asteroids approaching dangerously to our planet, the study of the orbits of these objects, etc. Appealing for a large audience among scientists are the subjects related to Chaos and Order as well as those centered on the study of the dynamics of exoplanets (extrasolar planets). The appeal of the more theoretical papers lies in the fact that they make a tour on the state-of-the-art of several classical problems.

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

This volume of proceedings contains research and review papers concerning the dynamics of asteroids and comets and especially their interactions with the Earth as signified by geological and historical records. Remembering what may have happened to the dinosaurs, but being careful to avoid creating irrational scares, the papers attempt to improve our knowledge of dynamics of the small objects of the Solar System and to assess in particular their effects on the Earth environment and the evolution of life. This book will be an up-to-date source of information to astronomers and dynamicists interested in the dynamics of small bodies of the Solar system, as well as to geologists and paleobiologists interested in the effects on the Earth of extraterrestrial bombardment by asteroids and comets.

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.

This book is intended to diffuse original research results interesting people working in Celestial Mechanics in both theory and applications. Theoretical investigators will find several results on Hamiltonian Dynamics, periodic Orbits, Chaos Diagnostic and Perturbations Theory. Applications cover several directions of research starting with those related to space exploration (mission design and space research) to those related to astronomy (extrasolar planets, asteroids, Near Earth asteroids). Since this book carries original results, it is unique and complements similar books and journals. Some of the subjects have great media appeal: the risk of impact of space debris on the Space Station, the possibility of fly-by missions to asteroids approaching dangerously to our planet, the study of the orbits of these objects, etc. Appealing for a large audience among scientists are the subjects related to Chaos and Order as well as those centered on the study of the dynamics of exoplanets (extrasolar planets). The appeal of the more theoretical papers lies in the fact that they make a tour on the state-of-the-art of several classical problems.

Fans of "Asterix the Gallic" know well that the only fear of people in Brittany is that the sky falls upon their head. So it must have been a shock for them (the fans of Asterix) to learn that a horde of Physicists and Dynamicists (some of them being actually Roman - ils sont fous ces Romains!) invaded the bay of Saint-Brieuc and spend a full week conjuring all the nastiness that the sky has in reserve, revelling in the horrors hidden beyond the blue dome; they talked with delight about "asteroids", "comets" and "meteor streams"; they grinned at the idea of "artificial satellites", these pots and pans of space always ready to fall upon you; some of them said strange things about the Moon, the planets, and evoked the "rings" of Saturn or of some other of their gods. One evening, a Roman from Pisa went as far as cornering some inhabitants in the large hut they used for their witchcraft and filled them with terror by describing the fate of the poor dinosaurs victims of a particularly nasty asteroid (or was it a comet?). You will be surprized to learn that Bretons did not exact a spectacular revenge for these offenses. On the contrary.

The success of the two first Alexander von Humboldt Colloquia on Celestial Mechanics (March 1984 and March 1988) encouraged us to meet again this year from March 29 to April 4, 1992 in the " Alpengasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was devoted to the "Qualitative and Quantitative behaviour of Planetary Systems". The papers covered a large range of questions of current interest from the behaviour of dust particles to the stability of the Solar System as a whole, without forgetting the motion of Asteroids and their classification into families. KAM theory, chaotic motions, resonances, Lyapunov characteristic exponents, perturbation theory, numerical integration were - of course - on the menu every day, served with sauces and accents from various part of the world: from China, from Brazil, from the United States and from all over Europe. To be able to organize this - now well established - meeting , we have to thank primarily the munificence of the Austrian Ministry of Science, furthermore the Steiermarkischen Wissenschafts- und Landesfonds and the Osterreichische Nationalbank for financial support.Also, the Osterreichische Forschungsgemein- schaft and the University of Vienna made it possible to invite participants to this meeting from abroad. Support in form of "Tagungsunterlagen" was given by the Creditanstalt-Bankverein in Vienna and coffee during the whole meeting time was donated by Homig-Kaffee Graz.

Minor bodies in the Solar System, though representing only a small fraction of the mass in the Solar System, may well play a fundamental role in terrestrial evolution.

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.

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.

The Workshop on Chaos in Gravitational N -Body Systems was held in La Plata, Argentina, from July 31 through August 3, 1995. The School of Astronomy and Geophysics of La Plata National University, best known as La Plata Observatory, was the host institution. The Observatory (cover photo) was founded in 1883, and it has nowadays about 120 faculty members and 70 non-faculty members devoted to teaching and research in different areas of astronomy and geophysics. It was very nice to see how many people, from young students to well recognized authorities in the field, came to participate in the meeting. This audience success was due to the increasing understanding of the neces­ sity to gather together people from Celestial Mechanics and Stellar Dynamics to explore the problems that exist at the frontier of these two disciplines and their common interest in chaotic phenomena and integrability (the famous Argentine beef was, certainly, also an attraction!). All the papers of the present volume were refereed. Most were accepted after some revision, while some needed no change at all (compli­ ments to their authors!) and, sadly, a few could not be included. About half a dozen authors did not submit their contributions for publication, mainly because they were already in print elsewhere. Therefore, the special issue of Celestial Mechanics and Dynamical Astronomy includes all the invited lectures of the workshop, while the proceedings volume includes those same lectures plus the bulk of, but Bot all, the contributions to the meeting.