David P. Feldman, Chaos and Dynamical Systems. Princeton University Press, 2019. ISBN: 9780691161525.
Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.
In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.
Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
Reviews
"
There is a significant and (I hope) growing genre in the physics
literature, that of the informative introductory book. Such a
book lands in the valley between two extremes of scientific
exposition. On the one hand, a popular book can often introduce
a nonexpert reader to a subject, with a focus on the big ideas
and the history of a field and the personalities that shaped
it. Such a book can, however, be frustrating owing to its lack
of detail and specific results about its field. On the other
hand, a standard textbook can be exhaustive in detail, but omit
the background thinking that gives the subject life and
meaning. Feldman's Chaos and Dynamical Systems deliberately and
deftly navigates the gap between these extremes."
"The greatest strength of this book is the logic and clarity of
the discussion. Each topic, each idea, is developed and
explained. ... A secondary strength is that Feldman places the
specific results in a broader context."
— John
L. Bohn, American
Journal of Physics
"David Feldman has written a gentle and loving introduction to
dynamical systems.... If you have not ever read anything about
dynamical systems and if a simple differential equation is your
friend (or future friend) then this book is for you. The
mathematics is clear and well-explained. The examples are as
simple as possible while still illustrating the points....
If, however, you are an expert on dynamical systems then this book
will not teach you anything new. Still, I would encourage
experts to read this book because Feldman’s writing style is so
gentle and clear that even experts will learn about expository
writing.
[T]his is an excellent introduction to chaotic systems with
well-written prose, clear examples, and a comprehensive list of
references for further reading. Chaos and Dynamical Systems is a
book for everyone from the layman to the expert. Each will find
it useful, informative, and a model of what a popular
mathematics book should be."
— David
S. Mazel, MAA
Reviews
"His approach is more on an intuitive basis, letting the reader be surprised by the results produced, and then asking (and answering) the questions that the reader naturally would ask: Why is it like that? How is this possible? ... With a minimum of mathematics, Feldman succeeds in introducing the reader to the world of dynamical systems and the, almost mythical, chaos that they can produce." — Adhemar Bulthell, European Mathematical Society..
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About the Author
Dave
Feldman is David Feldman is Professor of Physics and
Mathematics at College of the Atlantic. He is the author of
two books: Chaos and
Fractals: An Elementary Introduction (Oxford
University Press, 2012), a textbook for non-math/science majors;
and Chaos and Dynamical Systems (Princeton University Press,
2019), a contribution to the Primers in Complex Systems
series. Dave has developed two MOOCs, one on Chaos and Dynamical
Systems and one on Fractals and Scaling. These free, online
classes are part of the Santa Fe Institute's Complexity Explorer
project and have been taken by thousands of students. He is
currently working on a textbook on renewable energy.
Dave has taught over twenty different classes in physics, math, and computer science at College of the Atlantic. He served as COA's Associate Dean for Academic Affairs from 2003-07. Dave served as Co-director of the Santa Fe Institute's Complex Systems Summer School (CSSS) in Beijing, China from 2006-08 and since 2017 has directed the Santa Fe CSSS. From December 2018 to August 2019 he was the Interim Vice-President for Education at the Santa Fe Institute. Dave was a U.S. Fulbright lecturer in Rwanda in 2011-12.
Resources
This book is based partly on a free, online course of mine: Introduction to Dynamical Systems and Chaos. If you are teaching a class or reading on your own, you may find the material in this course of interest. This course is part of the Santa Fe Institute's Complexity Explorer project, which has made available a range of resources, including other courses and tutorials, in chaos and complex systems. The online course is, as of July 2023, ranked by classcentral.com fourth among over 2500 free online mathematics courses and is also among their top 250 online courses of all time.
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