Invitation to Dynamical Systems

by Edward R. Scheinerman

A textbook on dynamical systems, for sophomore-junior level students who want to continue exploring mathematics beyond linear algebra, but who may not be ready for highly abstract material. It presents both the "classical" theory of linear systems and the "modern" theory of nonlinear and chaotic systems; works with both continuous and discrete time systems; integrates computing into the text; and includes a wide variety of topics, such as bifurcation, symbolic dynamics, fractals, and complex systems. A collection of programs written in MATLAB is available as a supplement. Four stunning color plates (2pp.). Annotation copyright Book News, Inc. Portland, Or.

Genres: Mathematics

384 pages, Hardcover

First published August 4, 1995

Reviews

[Stuart Woolf · Rating 4 out of 5]

This book isn't as good as Strogatz's book - but, to its credit, it does include more math. The content is also more advanced, but only slightly so. I'll need to review Sarkovskii's theorem and symbolic dynamics before attempting the relevant problem sets, but it strikes me as manageable material. This review does not reflect Scheinerman's treatment of fractals, which interested me less than other subjects.

Personally, I felt the book's greatest strength was its review of linear algebra. The textbook I used in college, which I still have and reference regularly, introduced topics like eigenvalues, eigenvectors, diagonalizing, and Jacobians without ever building intuition behind them. This book does a very good job doing just that, so its worth your time for that reason alone.

[J. · Rating 3 out of 5]

I think this book has a good title. It is indeed an "Invitation." It manages to illustrate some of the cool ideas in DS without getting too technical. There's a lot of good things in here, illustrations and motivations, but I'm left wondering a little about the audience. The author tries to require as little mathematical sophistication as possible, but that's still quite a bit for this subject, including matrices and DEs. I think this would make a good supplement to a more rigorous book, or perhaps a good book for a mathematically sophisticated reader whose area of expertise was somewhere far away, but it's probably not ideal for someone wanting to really learn the topic.