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Introduction to Dynamical Systems, by Michael Brin, Garrett Stuck
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This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.
- Sales Rank: #2106328 in Books
- Published on: 2016-02-01
- Released on: 2015-11-05
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .63" w x 5.98" l, .80 pounds
- Binding: Paperback
- 256 pages
Review
"... an ideal choice for a graduate course on dynamical systems ... warmly recommended ..."
Acta Scientiarum Mathematicarum
"... exceptionally well written ... You should consider adopting this wonderful text for your next graduate course on the pure mathematics of the modern theory of dynamical systems."
Carmen Chicone, SIAM Review
"... despite the breadth, one finds here major results rigorously treated and substantial applications. By itself, the clean, accessible exposition of the amazing Sharkovsky theorem would justify the acquisition of this book ... Highly recommended."
Choice
"While the pace is fast and the book is very concise, the organization and selection of topics has been considered carefully, and the writing is strong enough to support the speedy treatment ... It certainly does give a notion of the scope of dynamical systems in a way that few other single books do."
Bill Satzer, MAA Reviews
About the Author
Michael Brin is Professor Emeritus of Mathematics at the University of Maryland. He is the author of over thirty papers, three of which appeared in the Annals of Mathematics, and he has lectured at conferences and universities around the world. His main research areas are dynamical systems and Riemannian geometry. In 2008, he established the Michael Brin Prize in Dynamical Systems.
Garrett Stuck is a former professor of mathematics at the University of Maryland and has held visiting positions at the Institut des Hautes Etudes Scientifiques in Paris and the Mathematical Sciences Research Institute in Berkeley. He has co-authored several textbooks, including The Mathematica Primer. Dr Stuck is also a founder of Chalkfree, Inc. He currently works in the finance industry.
Most helpful customer reviews
13 of 15 people found the following review helpful.
Great Survey Book
By Ryan P. Croke
So far I have found this book to include many of the classic and meaningful examples of Dynamical Systems, and has appropriate exercise for a graduate level course. So, I'll give it a good rating based soley on its use for researchers and advanced math students. However, it is very terse. Do not pick this up expecting a lot of discussion about the topics. Most of the time it is basically a list of definitions and theorem/proof's with exercises. Because of that it is great for use in a class, but might be a little difficult for independent learning. It could use a few more pictures, too.
9 of 10 people found the following review helpful.
Great expectations, unmet
By Narada
The author is a very good mathematician (and a grandfather of Google) so I was expecting a short and lucid introduction to dynamical system. Imagine my sadness when I found the book barely comprehensible. Apparently, the author learned his writing skills in Russian in the 60s, where paper was scarce, and any sort of explanation was viewed a waste thereof. If you actually want to understand dynamics, Katok/Hasselblatt Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) is vastly superior.
2 of 4 people found the following review helpful.
Our lecture notes
By stochasticmind
This book was mostly our lecture notes for a year long course at University of Maryland. We helped find typos in it and I have read most of this material very carefully.
It is exceedingly concise. It is a good introduction if you have access to classes themselves; otherwise, it is a rather quick way for an advanced reader to learn about some major topics in Dynamical systems. If you have time, everything is there and the book is readable. overall, a good book in your collection of dynamical systems but perhaps not the very first book on the subject. I would say it's good for a third year graduate student for self-study.
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