Date: Mon, 6 Nov 2006 From: "ADLUNG, Sonke" Subject: Classical and Quantum Chaos, Reports 1 & 2 I am attaching the reports we solicited on your book project. As you will see, the bottom line is clearly positive, and the referees are encouraging us to move ahead. Please let me know your reactions to the reports -------------------------------------- Report 1 ---------------------------------------- The authors have prepared a graduate-level textbook that aims to bridge the gap between the mathematical and physical approaches to nonlinear dynamical systems. The book is not intended to be an introduction to nonlinear dynamics. The authors in fact note that the readers need to have a modest background in the field, as might be provided by a number of standard books, to benefit from their treatment. Thus, the audience for the book will be limited to advanced graduate students in mathematics or the physical sciences (and perhaps experienced researchers in nonlinear dynamics) who wish to have a solid grounding in the methods of periodic-orbit (cycle) analysis. The authors are themselves experienced researchers in nonlinear dynamics and bring an authoritative perspective and tone to the project. For example, the sample first chapter reads like a (serious) conversation with a colleague who is willing to point out the difficulties as well as the power of the analysis. The treatment seems to be particularly up-to-date with the inclusion of a discussion of important computational techniques that are required to make use of the analytic developments. Although the foundations of periodic-orbit analysis have been known for many years, it is only recently that advances in both the analytic and computational techniques have made the application of these ideas possible for a wide range of interesting systems. Hence, I believe that the book makes an important and timely contribution to the literature of nonlinear dynamics. A distinctive feature of the book is its thorough treatment of quantum chaos in terms of periodic-orbit analysis. This area of study illuminates the boundary between the macroscopic and microscopic (quantum) worlds, helping to clarify concepts on both sides of the boundary. In addition, quantum chaos may turn out to be important in understanding both the potential and the problems with so-called quantum computers. I noticed one minor inconsistency: On page 9, the authors lay out the common strategy for analyzing dynamical systems in three stages: I. diagnose, II. count, III. measure. However, on page 26, the stages are given as 1) count, 2) weigh, 3) add up. The writing is generally well done and interesting. However, I did find a few minor typographical errors, indicating that the authors need to do a careful proofreading of the manuscript. Page 9, line 4, should read "it, it is not...." Page 12, 4 lines from bottom "system" should be "systems" Page 14, middle of the page "tolinear" should be "to linear" Page 19, middle of the page "that falls of the edge" should be "that falls off the edge" Page 22, 6 lines after Eq. (1.15), "retaced" should be "retraced" Page 25, line 6, should be "the theory of dynamical zeta ..." -------------------------------------- Report 2 ----------------------------------------- This is a very interesting and ambitious project by a respected and well-known researcher and his collaborators in the field for which the book is written. A version of the text has been on-line for a number of years, and I gather it has been used by the author for a graduate-level course covering these topics at Georgia Tech and in Europe. This is not a book for a first course in chaos or for the faint of heart, since it covers a wide range of topics with a high level of mathematical sophistication. I have no doubt that in the hands of the author, the course for which it was written is highly successful. It is less clear the extent to which it has been or would be adopted by others since courses on these topics tend to be somewhat individualized to the interests and abilities of the instructor, and there are competing texts at various levels and with different emphasis. The subject matter is of considerable current interest, although some of the chaos hype and consequent student interest has subsided over the past decade or so. The book attempts to cover some rather difficult topics using relatively high-level mathematics. The writing is clear and informal, sometimes sounding more like a lecture than a written treatise. Quotations and humor are sprinkled throughout. These techniques should help relieve the fear that the reader might otherwise have in plowing through the material. The topics covered include the major formal principles of nonlinear dynamical systems theory, but without many of the applications that might interest students and researchers. For example, there is relatively little on fractals, detecting chaos in experimental data, chaos control, spatiotemporal chaos, self-organization, high-dimensional and complex systems, and numerical methods. On the other hand, there is relatively much on quantum chaos that is largely lacking in other texts. I think this is a book that many researchers and upper-level students would like to own and that would be purchased by university libraries. How widely it will be adopted as a course text has to be seen. The subject is good and of considerable current interest, the level is high, the choice of topics may or may not coincide with the desires of other instructors, and there are some competing texts. ------------------------------------------------------------------------