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Proceedings of the Third 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.
The main theme of the book is the presentation of techniques used to identify chaotic behavior in the evolution of conservative mechanical systems and their application to astronomical systems. It results from graduate courses given by the author over the years both at university and at several international summer schools. Along the book surfaces of section, Lyapunov characteristic exponents, frequency maps, MEGNO, dense grid maps, etc., are presented and discussed in connection with the applications. The initial chapter is devoted to the presentation of the main ideas of the chaotic dynamics of conservative systems in plain language so that they can be accessible to a wide range of professionals and students of physical sciences. The applications are mainly related to the motions in the solar system and extrasolar planetary systems. Another chapter is devoted to the applications to asteroids showing how the asteroidal belt is sculpted by chaos and resonances. The contrasting existence of gaps in the distribution of the asteroids and groups of asteroids in resonances is thoroughly discussed. The interest in applications to planetary systems is growing since the discovery of systems of resonant planets around some stars of the solar neighborhood. Exoplanets added a lot of cases to a problem that was before restricted to the planets of our solar system. The book includes an account of results already existing about compact systems.
IAU Transactions are published as a volume corresponding to each General Assembly. Volume A is produced prior to the Assembly and contains Reports on Astronomy, prepared by each Commission President. The intention is to summarize the astronomical results that have affected the work of the Commission since the production of the previous Reports up to a time which is about one year prior to the General Assembly. Volume B is produced after the Assembly and contains accounts of Commission Meetings which were held, together with other material. The reports included in the present volume range from outline summaries to lengthy compilations and references. Most reports are in English.
The Alexander von Humboldt Colloquium on Celestial Mechanics (sub titled "The Stability of Planetary Systems") was held in Ramsau, Styria, in the Austrian Alps, from March the 25th to the 31st, 1984. The dedication of the meeting to Alexander von Humboldt presented partici pants with the challenge that the discussions during the week should reflect the spirit of that great scientist of the last century, that the very many interesting ideas presented and developed during the sessions should be interpreted in the light of a broad v~ew of astron omy and astrophysics. The topics of the meeting ranged from astrometric questions relating to the specification of inertial reference systems, motion of planets (including minor planets) and satellites, with the recurring topic of the search for criteria of stability of the systems, resonances, periodic orbits, and to the origin of the systems. Each session began with one or more invited review papers, followed by offered contributions and discussion. Three evening discussions were held, devoted respectively to inertial systems, to numerical integration techniques, and to cosmogonic problems and ring systems. On the evening of Wednesday, March 28th, a recital of chamber mus~c was given by Bernhard Piberauer, on the violin, and Meinhard Prinz, on the piano.