Introduction to Dynamical Systems 1st Edition by Michael Brin (PDF)

Description

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 such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I can understand the disparaging reviews of this book, but this book is a graduate textbook requiring significant mathematical maturity. Consequently, the author, in my opinion, is right to expect students of higher maths to fill in the blanks and mentally construct their own example. This book is my favorite as a comprehensive introduction to dynamical systems since it supplies enough details to help with pursuing research on the subject.

⭐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.

⭐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.

⭐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

⭐is vastly superior.

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