Chaos and Complexity in Astrophysics , Oded Regev , Cambridge U. Press, New York, 2006. $85.00 (455 pp.). ISBN 978-0-521-85534-1
Oded Regev’s Chaos and Complexity in Astrophysics does an excellent job of introducing nonspecialists to a wide range of topics in nonlinear dynamics. The first part of the book develops the subject in a methodical, step-by-step manner that is particularly well suited for graduate students. Regev, a professor of physics at Technion-Israel Institute of Technology, gives the essential details of such topics as bifurcation theory, strange attractors, fractals, and Hamiltonian systems in an easy-to-follow style that benefits greatly from the inclusion of representative examples.
In the spirit of a good introductory text, he omits unnecessary details and concentrates on the key points and important concepts, and he directs interested readers to the appropriate references for technical subtleties. Good demonstrations of his commendable approach are provided in discussions of nearly integrable systems and the Kolmogorov-Arnold-Moser theorem, fractal sets and dimensions, and patterns in spatially extended systems.
The second part covers astrophysical applications—and that is where the general topic, not the book itself, becomes somewhat problematic. The point is that, with the exception of a few isolated subfields, chaos theory actually has had a limited impact on most areas of astrophysical research. Such a state of affairs is, in fact, clearly reflected in the contents of Regev’s book. Despite its title, almost two-thirds of Chaos and Complexity in Astrophysics is devoted to basic explanations of dynamical systems in general, if one includes the discussions of fluid dynamics and convection, and only one-third to concrete applications to astrophysics. The break-down of the topics is not a consequence of astrophysicists being unaware of developments in nonlinear dynamics. Although Regev implicitly complains about astrophysicists resorting too quickly to brute-force computer simulations in situations in which insights might have been gained using a nonlinear-dynamics approach, reality is often more complex.
Many astrophysical systems are genuinely complicated; they involve numerous processes that operate on a huge range of physical and temporal scales. To pretend that those systems are governed by a simple, underlying mechanism described by a limited set of nonlinear equations is, in many cases, not only unproductive but also untrue. Thus problems such as large-scale structure formation or the dynamics of globular structures do require massive simulations. In those areas in which chaos theory has made significant contributions to astrophysics—for example, in the dynamics of the solar system, the theory of stellar pulsations, and the process of accretion onto compact objects—Regev’s description is generally comprehensive and very clear. He justifiably excludes chaotic inflation, in spite of its name, because it has nothing to do with chaos theory. I was, however, slightly disappointed by his omission of the more recent developments in the theory of convection, particularly the extensive works of Juri Toomre, Nic Brummell, and their collaborators.
Despite the relatively minor role that chaos theory has played so far in astrophysics, Chaos and Complexity in Astrophysics provides an important service by filling a gap in the description of nonlinear dynamics in existing astrophysical literature. Any researcher interested in dynamical systems in general, and in such systems in astrophysics in particular, will likely find something interesting in Regev’s book. And the fact that the text is essentially self-contained makes it attractive for graduate students to use.
