A First Course in Chaotic Dynamical Systems: Theory and Experiment

Studies in Nonlinearity

by Robert L. Devaney

A First Course in Chaotic Dynamical Theory and Experiment, Second EditionThe long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics.The area of dynamical systems covered in A First Course in Chaotic Dynamical Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses.FeaturesMore extensive coverage of fractals, including objects like the Sierpinski carpet and othersthat appear as Julia sets in the later sections on complex dynamics, as well as an actualchaos "game."More detailed coverage of complex dynamical systems like the quadratic familyand the exponential maps.New sections on other complex dynamical systems like rational maps.A number of new and expanded computer experiments for students to perform.About the AuthorRobert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.

Genres: Science, Mathematics, Textbooks, Reference

318 pages, Kindle Edition

First published August 1, 1992

Reviews

[Logan Kennedy · Rating 4 out of 5]

This book was a great and interesting mathematics book. Robert L. Devaney did an amazing job at explaining complex ideas to the audience. Each chapter and each topic, he helps walk you through it step by step. He also does a great job at explaining and showing why things are the way that they are. Not only is his writing good on helping you understand, but the whole field of these forms of mathematics are some of the most interesting and applicable ideas in modern day technology. This adds the feeling of actually being able to use what you are learning. It is also a nice compliment that he adds experiments in the book that you can try out yourself. I personally would recommend this book for people who are genuinely interested in mathematics and similar subjects. Overall, I found this book very interesting and worth a read if you are interested.

[Brian Bloom · Rating 3 out of 5]

I took a course on Chaos Theory and just wasn't a fan at all but that isn't the book's fault