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.

At the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events. The conference room is called "Salone degli Svizzeri": here, Gregory XIII, on February 24, 1582, gave its sanction to the reform of the Julian calendar and declared officially in use the calendar still adopted nowadays. The magnificent high walls and tall ceiling strongly resounded, giving to our voice a peculiar Vatican sound, which took us by surprise. May be - we thought - a distant echo of the very words of Gregory XIII proclaiming the modem calendar was still haunting the room. Around us, in the audience, many countries were represented, thus indicating that the idea of putting together the three "souls" of modem Celestial Mechanics - perturbation theories, solar and stellar system studies, spaceflight dynamic- had been successful. CELMEC III is in fact the latest of a series of meetings (the first two editions took place in 1993 and 1997 in L' Aquila, Italy) whose aim is to establish a common ground among people working in Celestial Mechanics, yet belonging to different institutions such as universities, astronomical observatories, research institutes, space agencies and industries.

A primer for researchers and graduate students; introduces and applies chaos techniques to specific astrophysical systems.

Molecular dynamics is a well-established technique for simulating complex many-particle systems in many areas of physics, chemistry, and astrophysics. The huge computational requirements for simulations of large systems, especially with long-range forces, demand the use of massively parallel computers. Designing efficient algorithms for these problems is a highly non-trivial task. This book contains the invited talks and abstracts presented at a conference by more than 100 researchers from various fields: computer science, solid state physics, high energy physics, polymers, biochemistry, granular materials and astrophysics. Most of the contributions have been written by users of massively parallel computers and deal with practical issues, but there are also contributions tackling more fundamental algorithmic problems.

This book contains essays in honour of Claus Weddepohl who, after 22 years, is retiring as professor of mathematical economics at the Department of Quantitative Economics of the University of Amsterdam. Claus Weddepohl may be viewed as th~ first Dutch mathematical economist in the general equi librium tradition of Arrow, Debreu and Hahn. The essays in this book are centered around the themes Equilibrium, Markets and Dynamics, that have been at the heart of Weddepohl's work on mathematical economics for more than three decades. The essays have been classified according to these three themes. Admittedly such a classification always is somewhat arbitrary, and most essays would in fact fit into two or even all three themes. The essays have been written by international as well as Dutch friends and colleagues including Weddepohl's former Ph. D. students. The book starts with a review of Claus Weddepohl's work by Roald Ramer, who has been working with him in Amsterdam for all those years. The review describes how Weddepohl became fascinated by general equilibrium theory in the early stages of his career, how he has been working on the theory of markets throughout his career, and how he turned to applications of nonlinear dynamics to price adjustment processes in a later stage of his career. The first part of the book, Equilibrium, collects essays with general equilib rium theory as the main theme.

With the bulk of asteroids floating in space between the orbits of Mars and Jupiter, astronomers puzzle over where these rocks came from. Are they the remnants of a planet? Excess not used in the formation of the Solar System? Nothing more than random bits of debris? The location of the belt makes for a quasi-barrier separating the inner from the outer planets. Perhaps asteroids were meant to discourage human space exploration. NASA has sent missions to explore the asteroid belt and the rocks themselves, and those missions have yielded some interesting observations on the composition of the asteroids but no definitive answer as to their origin. Earth-based tools such as telescopes and satellites also contribute to asteroid research but cannot plumb the depths behind these varied chunks of flotsam. Presented in this book is a list of carefully chosen abstracts and citations of relevant literature about asteroids and the research into them. Prior to this listing, though, comes an overview of the nature of the asteroids and what we know now about them and what we hope to discover in the future. lifeless but mysterious rocks inhabiting the solar system. To conclude, easy access is provided through author, title, and subject indexes.

This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.