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# Chaos: An Introduction to Dynamical Systems (Textbooks in Mathematical Sciences) [Paperback]

Kathleen T. Alligood , Tim D. Sauer , James A. Yorke

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## Book Description

October 1, 2000 0387946772 978-0387946771 Corrected
Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.

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## Editorial Reviews

### Review

From the reviews:

"… Written by some prominent contributors to the development of the field … With regard to both style and content, the authors succeed in introducing junior/senior undergraduate students to the dynamics and analytical techniques associated with nonlinear systems, especially those related to chaos … There are several aspects of the book that distinguish it from some other recent contributions in this area … The treatment of discrete systems here maintains a balanced emphasis between one- and two- (or higher-) dimensional problems. This is an important feature since the dynamics for the two cases and methods employed for their analyses may differ significantly. Also, while most other introductory texts concentrate almost exclusively upon discrete mappings, here at least three of the thirteen chapters are devoted to differential equations, including the Poincare-Bendixson theorem. Add to this a discussion of $\omega$-limit sets, including periodic and strange attractors, as well as a chapter on fractals, and the result is one of the most comprehensive texts on the topic that has yet appeared." Mathematical Reviews

## Product Details

• Series: Textbooks in Mathematical Sciences
• Paperback: 604 pages
• Publisher: Springer; Corrected edition (October 1, 2000)
• Language: English
• ISBN-10: 0387946772
• ISBN-13: 978-0387946771
• Product Dimensions: 1.2 x 6.9 x 9.1 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review:
• Amazon Best Sellers Rank: #611,145 in Books (See Top 100 in Books)
• #60
• #68

## Customer Reviews

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27 of 29 people found the following review helpful
5.0 out of 5 stars great introduction to dynamical systems June 11, 1998
By A Customer
Format:Paperback
I was enrolled in a course at GMU in which the draft version of this text was used. The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math. The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be. Many of the systems can be modeled on a spreadsheet. If you have any interest in Chaos, this book will only strengthen it.
24 of 26 people found the following review helpful
5.0 out of 5 stars For my Taste One of the Best Undegraduate Texts February 12, 1998
By A Customer
Format:Paperback
This book presents brilliantly the foundations to Dynamical Systems and Chaos. You need to have some Linear Algebra, Calculus and Multivariable Calculus and Differential Equations knowledge. Full of exercises, computer experiments and Challenges. I think that the text looses some substance due to the lack of presenting more or all the solutions to the Exercises. They should be solved detailed in a Solutions Manual. Don't try to e-mail the authors for more solutions, they will not get them to you. This point is the only pitty in a text that is a great companion through chaotic dynamics. Also Very Brilliant for me at this Level are: Strogatz-Nonlinear Dynamics and Chaos, Kaplan-Understanding Nonlinear Dynamics, Gulick-Encounters with Chaos, Hilborn-Chaos and Nonlinear Dynamics, Devaney-An Introduction to Chaotic Dynamical Systems and A First Course to Chaotic Dynamics, Holmgren-A First Course in Discrete Dynamical Systems. More sofisticated maths but not too far away are: Schuster-Deterministic Chaos(graduate) and Ott-Chaos in Dynamical Systems (graduate).
11 of 12 people found the following review helpful
5.0 out of 5 stars Exciting and Lucid Introduction to Chaos Theory March 20, 2005
Format:Paperback
This book is a must-own for anyone interested in nonlinear dynamics and chaos -- I also highly recommend the "Nonlinear Dynamics and Chaos" text by Strogatz.

I especially like the numerous diagrams that clarify everything so well in this book. In addition, the writing includes just the right amount of informal discussion to truly explain the material without retreating into jargon.

A favorite moment in the book is a "challenge" exercise that explains the famous "Period Three Implies Chaos" result: the reader is gently guided through 10 steps resulting in a proof of Sharkovskii's Theorem, a more general result that includes the Period 3 thing as a special case.

11 of 13 people found the following review helpful
5.0 out of 5 stars The definitive guide to dynamical systems! October 7, 2000
Format:Paperback
When I purchased this book three years ago, I had only a rudimentary understanding of dynamical systems. Thankfully, all that was needed to get me started was some intermediate calculus and some basic college-level linear algebra. Since I had been doing both from the time I was a sophmore in high school, I had no trouble getting comfortable with it. The authors present dynamical systems in an easy-to-read style with tests that appear at the end of each chapter after you've had time to catch on.

If you're seriously thinking about getting started in dynamical systems, get this book!
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Books on Related Topics

 Nonlinear Dynamics And Chaos by Steven H. Strogatz Discusses: Chaos in Dynamical Systems by Edward Ott Discusses: Fractal Geometry by K. J. Falconer Discusses: Introduction to the Modern Theory of Dynamical Systems by A. B. Katok