Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers [Hardcover]

Robert C. Hilborn (Author)

Book Description

Publication Date: January 6, 1994 | ISBN-10: 0195057600 | ISBN-13: 978-0195057607 | Edition: annotated edition

This is the only book that introduces the full range of activity in the rapidly growing field of nonlinear dynamics to an audience of students, scientists, and engineers with no in-depth experience in the area. The text uses a step-by-step explanation of dynamics and geometry in state space as a foundation for understanding nonlinear dynamics. It goes on to provide a thorough treatment of such key topics as differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers), the surprising role of number theory in dynamics, and an introduction to Hamiltonian dynamics. This is the only book written at this introductory level to include the increasingly important field of pattern formation, along with a survey of the controversial questions of quantum chaos. Important analytical tools, such as Lyapunov exponents, Kolmogorov entropies, and fractal dimensions, are treated in detail. With over 200 figures and diagrams, and both analytic and computer exercises following every chapter, the book is ideally suited for use as a text or for self-instruction. An extensive collection of annotated references brings the reader into contact with the literature in nonlinear dynamics, which the reader will be prepared to tackle after completing the book.

Editorial Reviews

Review

"While the last few years have seen a flood of new books about chaos, the present volume is virtually unique in the breadth of its coverage and the relatively modest mathematical background it requires from its readers. . .I know of no better introduction to the subject." --Mathematical Reviews

"This ambitious book introduces a broad variety of concepts in nonlinear dynamics to an undergraduate audience....Contains much valuable material....Contains many computer examples and exercises that are useful and specific. It also has an extensive bibliography, which is a wonderful resource....Extremely useful. It provides lucid expositions of many important concepts as well as an extensive introduction to the literature of nonlinear dynamics." --Susan Coppersmith, ATandT Bell Laboratories, Computers in Physics

"I congratulate the author on having managed to write an extremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self-explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner, and...he succeeds in conveying a complete and satisfying picture....Often I felt as if the author in person was guiding me through the amazing and beautiful world of chaos ....Hilborn somehow knows how to get important points across with the barest minimum of necessary mathematics.... Hilborn's book is a thorough and well-written introduction to nonlinear dynamics. I strongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject." --Earle R. Hunt, Ohio University, IEEE Spectrum

About the Author

Robert C. Hilborn, Lisa and Amanda Cross Professor of Physics, Amherst College.

Product Details

• Hardcover: 672 pages
• Publisher: Oxford University Press, USA; annotated edition edition (January 6, 1994)
• Language: English
• ISBN-10: 0195057600
• ISBN-13: 978-0195057607
• Product Dimensions: 9.4 x 6.4 x 1.9 inches
• Shipping Weight: 3 pounds
• Average Customer Review: 4.6 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #1,932,283 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

5.0 out of 5 stars A excellent introduction to chaos, November 24, 2003

By 

Willard L. Maier (Texas) - See all my reviews
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This review is from: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Hardcover)

This is an accessible and readable introductory textbook on chaos and nonlinear dynamics. It focuses on the ideas behind the theory of chaos, rather than on the details of the mathematics which can sometimes hinder rather than help the reader gain real insight into the mechanisms of nonlinear systems.

By this I do not mean that the author skips over the required mathematics. The text is intended for people with a solid background in differential equations, and some familiarity with classical dynamical systems is also helpful if not completely necessary. I would say it is targeted for advanced undergraduate or beginning graduate students in the mathematical sciences, as well as scientists/engineers with no background in chaos theory. However he does not get bogged down in mathematics at the expense of physical insight. I have been studying the book on my own and have run into few problems in understanding the explanations.

The first chapter goes over 3 chaotic systems as a practical way of introducing the reader to various features of such systems. This provides a basis of practical experience to draw upon for the rest of the book, where the principles of chaos are examined in greater detail. The extensive references given in the book are a valuable addition that can be used to further explore the scientific literature. The references include journal papers as well as books, articles, and software for dynamical systems.

If you have the requisite mathematical background and want to learn the basics of chaos and nonlinear dynamics, I highly recommend this book.

17 of 21 people found the following review helpful:

5.0 out of 5 stars fundamental, systematic, November 6, 2001

By 

King David (Hong Kong) - See all my reviews

This review is from: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Paperback)

If you are looking for a textbook or reference on chaos theory, I recommend you to buy this book.

If you read other books, you will eventually comment,'chaos is something related to mathematics, very abstract, has nothing to do with my messy bedroom...'

But if you read this book, you will scream,'Great! I have figured out the richness of the nonlinear world. I understand the different dynamical routes to chaos. I know different quantifying methods with their pros and cons. Most fascinating is that chaos is related to pattern formation and self organization, which I consider them as another field of knowledge before. Also chaos may provide a new approach to quantum mechanics, a good news for those including me who do not believe in the parallel universe interpretation. By the way, I learnt a lot from this book!'

2 of 3 people found the following review helpful:

5.0 out of 5 stars An excellent introduction, March 8, 2007

By 

Udaya Kiran Jagadisan (Syracuse, NY USA) - See all my reviews
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This review is from: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Paperback)

Covers the basics in an in-depth manner, and exposes the reader to a wide range of exciting problems in dynamical systems theory. THE book to start with if one is interested in chaos.