Invitation to Dynamical Systems

by Edward R. Scheinerman

Designed for those wishing to study mathematics beyond linear algebra but unready for abstract material, this "invitation" to the excitement of dynamical systems appeals to readers from a wide range of backgrounds. Rather than taking a theorem-proof-corollary-remark approach, it stresses geometry and intuition. Topics include both the classical theory of linear systems and the modern theory of nonlinear and chaotic systems as well as bifurcation, symbolic dynamics, fractals, and complex systems.
In addition to offering a unified presentation of continuous and discrete time systems, this treatment integrates computing comfortably into the text. Appendixes feature important background material, including a gentle introduction to differential equations and explanations of how to write MATLAB, Mathematica, and C programs to compute dynamical systems. Prerequisites for advanced undergraduates and graduate students include two semesters of calculus and one semester of linear algebra.

Genres: Mathematics

408 pages, Paperback

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.