Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

By Robert C. Hilborn

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.

• Format: Hardcover
• Language: English
• ISBN: 0195057600
• ISBN13: 9780195057607
• Release Date: January 1994
• Publisher: Oxford University Press
• Length: 672 Pages
• Weight: 2.55 lbs.
• Dimensions: 9.6" x 1.5" x 6.8"

Customer Reviews

A good book for introduction

I have recently bought this book. I have been studying on evolution of the test particles in a particular planewave spacetimes, and I have realized that the system admits a non-integrable structure. I should investigate whether the particle motion emerges chaos or not. But, my knowledge on chaos was almost zero, before buying this book. Now, I am going to complete the full analysis of the book, and I am much more familiar to the concept of chaos. However, this book can be used for just begining. To proceed to the advanced problems you should look for other materials, especially to the articles about chaos. I advise this book as a first book to start chaos. Dr. Izzet Sakalli

An excellent introduction

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.

A excellent introduction to chaos

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.

fundamental, systematic

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!'

Good book!

If you want to get on into chaos, just read this book. I especially like the very wide scope of the subjects considered and the insight provided by the author in pattern formation or quantum chaos.