Book review

The chaotic dynamics was born at about the beginning of our century, with the works of the French mathematician Henri Poincaré on celestial mechanics (namely on the orbits of the restricted three-body problem). Nevertheless, the interest for this part of science grew rapidly especially in the last three decades, when it turned out that chaos could be present, also, in more "terrestrial" problems, as the motions of the atmosphere, the vibrations of machines, a.o. There are a lot of excellent monographs and textbooks on the subject of chaos. The point is that most of them are addressed to a mathematician reader. But now the chaos is important for many branches of science and technology, some of them having very few things in common with mathematics. It is clear that for the readers from these fields there are necessary special kinds of textbooks, where the mathematical information to be presented in all the details. Just such a kind of textbook is this one, written by an expert in the field. The book grew from several courses given by the author at the University of Maryland and is intended for use in graduate courses for scientists and engineers.

The contents table of the book is very detailed and it is no room here to describe it. In exchange, I will quote some of the topics touched. Thus, the reader can find informations about: attractors, one-dimensignal maps, fractals, Hausdorff dimension, stable and unstable manifolds, Lyapunov exponents, entropy, controlling chaos, chaotic scattering, Hamiltonian systems, KAM tori, the transition to chaos, unstable periodic orbits, quantum chaos, and many, many others. Homework problems and worked examples are included throughout the book.

Unlike other books of chaos, this one contains mere basic mathematics, usually unfamiliar to the readers it is addressed. The style is very pedagogical, so that its first goal, to be appropriate as a textbook for graduate courses for scientists and engineers, is, no doubt, attained. But it is, also, to be recommended as textbook for undergraduate courses for mathematicians. If someone wishes to learn chaotic dynamics, this is the book to start with. On the other hand, its broad coverage makes it useful as a reference for workers in the field, as well. There are, of course, other applications-oriented books on chaos (e.g. Gutzwiler - Chaos in Classical and Quantum Mechanics, springer, 1990), but, in general, their coverage is much narrow.

To finish, I ought to add that there is an extensive list of references, at the end of the book, and an index, too. The book is in excellen graphical conditions and contains many pictures and line diagrams.