Enhanced descriptions from Syndetics:

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Table of contents provided by Syndetics

• How to Identify Chaotic Vibrations
• Models for Chaos
• Maps and Flows
• Chaos in Physical Systems
• Experimental Methods in Chaotic Vibrations
• Criteria for Chaotic Vibrations
• Fractals and Dynamical Systems
• Spatiotemporal Chaos
• Appendices
• References
• Author Index
• Subject Index

Reviews provided by Syndetics

CHOICE Review

Barely a decade since the publication of Benoit B. Mandelbrot's The Fractal Geometry of Nature (1982), there are now books on fractals, chaos, and nonlinear processes numbering in the hundreds, some for the general reader, others targeted at special audiences ranging from mathematicians, natural scientists, and engineers, to economists, philosophers, and artists. The four volumes under review are indicative of this diversity. Moon's book is, perhaps, best suited for practicing engineers who wish to decide whether learning chaos theory will be relevant and profitable to their work. The many examples of engineering applications where chaos has been observed form the soul of the book. The noteworthy Chapter 2 offers broad heuristics for identifying chaotic phenomena in the laboratory. Actually a rewrite of the author's Chaotic Vibrations (CH, Jun'88), the book has grown to nearly twice its former size from the addition of exercises, new physical applications, and more mathematical explication. The mathematics remains vague, even though the reader must have some mathematical sophistication. As such, this book cannot be recommended for those who need to learn the details of the subject. The editing is haphazard. For example, one meets Feigenbaum's number, as though for the first time, on four occasions, the index noting only the first three. By contrast, Peitgen, Jurgens, and Saupe's book serves the mathematical neophyte who craves a deep knowledge of the mathematical foundations of chaos. This is an extremely leisurely, careful, detailed, copiously illustrated exposition. Not a popularization, it nevertheless should find the wide audience that is usually served only by diluted accounts. It is hard to think of another book like it, but then no other mathematical subject has ever so captured the public imagination. There is also much here for mathematically sophisticated readers and it is easy to find what interests one and to dig in. With its beautiful design, superb organization, and clear style, it is not premature to declare this book a classic. Some overlap notwithstanding, this volume does not supercede The Science of Fractal Images ed. by Peitgen and Saupe (CH, Mar'89) or Peitgen and P.H. Richter's The Beauty of Fractals (CH, Dec'86). Given the nearly one thousand pages, the low price is worthy of note. The raison d'etre of Field and Golubitsky's work must be the stunningly beautiful color plates of some new types of fractal images. The mathematical genesis of these images is the question that asks when the orbits of a dynamical system statistically exhibit the symmetries of the system as a whole. Remarkably, the answer may change from ^D" to ^D" as one varies a parameter-describing system; a real world example (that the authors leave underdeveloped) is wobbly train wheels that wear unevenly at slow speeds, evenly at high speeds. The abstract ideas, together with the basics of chaos theory and group theory, do receive a passable treatment, some in the text, some in technical appendixes that also give full details on the construction of the images. Unfortunately, the text is also full of uninspired generalities about symmetry and chaos and unconvincing comparisons with images from art and nature that bare superficial resemblance to these fractals. Finally, Briggs's is a popular account full of the grandiose ^D" posturing that gives chaos theory a bad name in some circles. Nevertheless, it does collate some interesting information and many fascinating and beautifully produced images. This book is not appropriate for academic libraries; this is the first book about fractals this reviewer has seen that does not contain a single equation. For coffee tables only. D. V. Feldman University of New Hampshire

Author notes provided by Syndetics

About the author FRANCIS C. MOON is a professor at Cornell University in the Sibley School of Mechanical and Aerospace Engineering. He served as Director of this school for five years and was also Chairman of the Department of Theoretical and Applied Mechanics. He is an Associate Editor of the journal, Chaos, and the author of Magneto-Solid Mechanics and a forthcoming book, Superconducting Levitation and Bearings. Dr. Moon received his PhD in theoretical and applied mechanics at Cornell University and taught for seven years at Princeton University before returning to Cornell. In addition to his many published papers in chaos, Dr. Moon has lectured at over 60 universities in North America, Europe, and Asia, and given numerous short courses in chaos and fractals to several corporations and government laboratories. His chaos experiments have also appeared on the PBS program, "Nova."