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An Introduction to Chaotic Dynamical Systems, 2nd Edition Paperback – January, 2003

10 customer reviews
ISBN-13: 978-0813340852 ISBN-10: 0813340853 Edition: Second Edition

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Editorial Reviews

Review

"This book provides a wonderful introduction to the subject...I strongly recommend it." -- Philip Holmes, Cornell University

About the Author

Professor Robert L. Devaney received his A.B. from Holy Cross College and his Ph.D. from the University of California at Berkeley in 1973. He taught at Northwestern University, Tufts University, and the University of Maryland before coming to Boston University in 1980. He served there as chairman of the Department of Mathematics from 1983 to 1986. His main area of research is dynamical systems, including Hamiltonian systems, complex analytic dynamics, and computer experiments in dynamics. He is the author of An Introduction to Chaotic Dynamical Systems, and Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, which aims to explain the beauty of chaotic dynamics to high school students and teachers.

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Product Details

  • Series: Studies in Nonlinearity
  • Paperback: 360 pages
  • Publisher: Westview Press; Second Edition edition (January 2003)
  • Language: English
  • ISBN-10: 0813340853
  • ISBN-13: 978-0813340852
  • Product Dimensions: 9.1 x 6.1 x 0.8 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #954,895 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 26 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on August 10, 2001
Format: Hardcover
This book gives a quick and elementary introduction to the field of chaotic dynamical systems that could be read by anyone with a background in calculus and linear algebra. The approach taken by the author is very intuitive, lots of diagrams are used to illustrate the major points, and there are many useful exercises throughout the book. It could serve well in an undergraduate mathematics course in dynamical systems, and in a physics undergraduate course in advanced mechanics. The author emphasizes the mathematical aspects of dynamical systems, and readers will be well prepared after finishing it to read more advanced books on dynamical systems.
Chapter 1 introduces one-dimensional dynamics, with the analysis of the quadratic map given particular attention. Called the logistic map in some circles, this very important dynamical system has been the subject of much study, and exhibits generically the properties of chaotic dynamical systems. The author also gives a brief review of some elementary notions in calculus needed for the chapter, making the book even more accessible to a wider readership. The important concept of hyperbolicity is discussed in the context of one-dimensional maps and a good discussion is given on symbolic dynamics. Structural stability, which is really useful only in dynamical systems in higher dimensions, is treated here. The intuition gained in one-dimension is invaluable though before moving on to higher-dimensional examples. Sarkovskii's theorem, which states that a one-dimensional dynamical system with a period three periodic orbit has periodic orbits for all other periods, is proved in detail. In addition, the Schwarzian derivative, so important in complex dynamics, is defined here.
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11 of 11 people found the following review helpful By Alexander C. Zorach on September 13, 2005
Format: Paperback
This book is an introduction to dynamical systems defined by iterative maps of continuous functions. It doesn't require much advanced knowledge, but it does require a familiarity and certain level of comfort with proofs. The basic idea of this book is to explore (in the context of iterative maps) the major themes of dynamical systems, which can later be explored in the messier setting of differential equations and continuous-time systems. While this book doesn't discuss differential equations directly, the techniques used here can be transferred (with considerable work and thought) to that setting. Someone wanting an elementary book covering differential equations as dynamical systems might want to check out the excellent multi-volume work by J. Hubbard; the combination of that work with this book would provide the background to tackle the tougher and less-accessible texts dealing with chaotic systems of differential equations.

Although this is a pure math book, the book does mention key applications and motivation behind the material; applied mathematicians will find this book quite useful, not necessarily because of the choice of topics but just because it greatly helps develop ones' intuition. The material is presented in a way that gives the student a sense of the big picture--what the theorems mean, how they fit together. Proofs are rigorous but as easy to follow as I have seen them in this subject.

The choice and order of subjects is also both practical and fun. The book begins with 1-dimensional systems and explores just about everything interesting that happens with them (including Sarkovski's Theorem, one of the most bizarre and surprising mathematical results), before moving into two-dimensions and then dynamics in the complex plane.

The bottom line?
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9 of 10 people found the following review helpful By A Customer on June 25, 2000
Format: Hardcover
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have any problem absorbing this material and is highly recommended to whom wants to know about the theory of chaos from the scratch.
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8 of 10 people found the following review helpful By A Customer on June 25, 2000
Format: Hardcover
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have any problem absorbing this material and is highly recommended to whom wants to know about the theory of chaos from the scratch.
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2 of 2 people found the following review helpful By Susan J. Calderon on March 8, 2007
Format: Paperback Verified Purchase
This is a very good book. Actually, Devaney's "First Course in Chaotic Dynamical Systems," is a good accompanying text. Fascinating subject...
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