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Book review

Author(s) Moon, Francis C.
Title Chaotic and Fractal Dynamics. An Introduction for Applied Scientists and Engineers
Publisher John Wiley & Sons
Year of publication 1992

This monograph deals with the applications of the nonlinear dynamics into investigations of the physical systems. For example, the concrete uses of the new geometric and topological concepts as applied to the theories of rigid body systems, elastic mediums, geomechanical processes, electrical and magnetic circuits, acoustic chaos, chemical reactions, biological membranes are given in detail. The book examines another interesting topics concerning with chaos. Introduction to classical nonlinear dynamics is presented using specifically the nonlinear vibration theory. Experimentalist's view of chaotic dynamics is discussed. The main tools for construction of the models for chaos is elucidated within the framework of maps and flows. The theory of fractals is described together with application of one in the physical sciences.

The book is organized in the following way. There are eight chapters: 1. Introduction: a new age of dynamics, 2. How to identify chaotic vibrations, 3. Models for chaos; maps and flows, 4. Chaos in physical systems, 5. Experimental methods in chaotic vibrations, 6. Criteria for chaotic vibrations, 7. Fractals and dynamical systems, 8. Spatiotemporal chaos. The book has the four appendices: A. Glossary of terms in chaotic and nonlinear vibrations, B. Numerical experiments in chaos, C. Chaotic tools, D. Books on nonlinear dynamics, chaos and fractals. Ones contain very useful additional information. The detailed explanation of 70 terms is given in appendix A. The profitable description of the chaotic toys is presented in the appendix C. All ideas in the book are depicted in 264 black pictures and 16 color plates. Exercises at the end of every chapter (all together 89) constitute the essential part of the book and ones make the book more suitable for students.

This book is written for reasearchers in the area of chaotic dynamics and its applications, for engineers, and for graduate students in this field. This text aims to provide the reader with a working knowlege of the fractals and nonlinear analysis of the dynamical systems. The methods presented in this book are widely applicable for the different phenomena.

All in all, Chaotic and Fractal Dynamics should be in any complete mathematical library of all mathematicians, who are interested in modern applications of the new mathematical ideas in nonlinear dynamics and purchase of this book is a good investment.