From Newton To Chaos

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.

With his critically acclaimed best-sellers The Mathematical Toursist and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clockwork image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages--from the star charts of ancient navigators to the seminal discoveries of the 17th centure; from the crucial work of Poincaré to the startling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history, and intellectual adventure.

'Gribbin takes us through the basics with his customary talent for accessibility and clarity' Sunday Times The world around us can be a complex, confusing place. Earthquakes happen without warning, stock markets fluctuate, weather forecasters seldom seem to get it right - even other people continue to baffle us. How do we make sense of it all? In fact, John Gribbin reveals, our seemingly random universe is actually built on simple laws of cause and effect that can explain why, for example, just one vehicle braking can cause a traffic jam; why wild storms result from a slight atmospheric change; even how we evolved from the most basic materials. Like a zen painting, a fractal image or the pattern on a butterfly's wings, simple elements form the bedrock of a sophisticated whole. Synthesizing chaos and complexity theory for the perplexed, Deep Simplicity brilliantly illuminates the harmony underlying our existence.

One CD-ROM disc in pocket.

The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines, including the humanities. In this volume, fourteen theorists explore the significance for literary and cultural studies of the new paradigm of chaotics, forging connections between contemporary literature and the science of chaos. They examine how changing ideas of order and disorder enable new readings of scientific and literary texts, from Newton's Principia to Ruskin's autobiography, from Victorian serial fiction to Borges's short stories. N. Katherine Hayles traces shifts in meaning that chaos has undergone within the Western tradition, suggesting that the science of chaos articulates categories that cannot be assimilated into the traditional dichotomy of order and disorder. She and her contributors take the relation between order and disorder as a theme and develop its implications for understanding texts, metaphors, metafiction, audience response, and the process of interpretation itself. Their innovative and diverse work opens the interdisciplinary field of chaotics to literary inquiry.

This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, presenting all the central concepts and equations at an accessible level. Chapters 1 to 4 contain the standard material of courses in theoretical physics and are supposed to accompany lectures at the university; thus they are rather condensed. They are supposed to fill one year of teaching. Chapters 5 and 6, in contrast, are written less condensed since this material may not be part of standard lectures and thus could be studied without the help of a university teacher. An appendix on elementary particles lies somewhere in between: It could be a summary of a much more detailed course, or studied without such a course. Illustrations and numerous problems round off this unusual textbook. It will ideally accompany the students all along their course in theoretical physics and prove indispensable in preparing and revising the exams. It is also suited as a reference for teachers or scientists from other disciplines who are interested in the topic.