Overview

Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that we are presenting a rather drastic revision of the first edition of the averaging book. The chapters have been updated and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams. Old proverb: one picture is worth a thousand words. The book includes an extensive bibliography and a detailed index. Format and printing are of the high standard common to Springer books. In conclusion, the authors completely achieve their goal and present their case in a concise manner. The book offers an effective entrance into a lively area of research and will be very valuable for those who study and do research in the field of asymptotic methods.

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