Chaos

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Summary: great introduction to dynamical systems
Review: I was enrolled in a course at GMU in which the draft version of this text was used. The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math. The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be. Many of the systems can be modeled on a spreadsheet. If you have any interest in Chaos, this book will only strengthen it.

Rating:
Summary: Look no further for your first intro to the subject!
Review: It's now been a decade since the time of a college course on Chaos and Fractals, when the textbook "Fractals Everywhere" by Michael F. Barnsely was used for teaching our class. For the several ensuing years the subject leapt into the background as I persued my studies in physics and later on in pure mathematics. Recently I have regained interest in some applied subjects such as dynamical systems and chaos, control theory, symplectic geometry, and information theory. Indeed the book by Alligood, Sauer, and Yorke was a somewhat recent recommendation by a college professor who had taught his students from it. I recall at the time there was a discussion as to whether Robert Devaney's book would have made for a better first course. He mentioned that Devaney only deals with the discrete dynamical systems, while ASY treats both discrete and continuous, and so the choice was clear. The topics discussed in the 13 chapters of the book include: one and two dimensional maps, fixed points, iterations, sinks, sources, saddles, Lyapunov exponents, chaotic orbits, conjugacy, fractals and their dimension, chaotic attractors, measure, Lotka-Volterra models, Poincare-Bendixson theorem, Lorentz and Roessler attractors, stable manifolds and crises, homoclinic and heteroclinic points, bifurcations, and cascades. There're also answers and solutions to the selected exercises, as well as extensive references at the back, making up an ideal setting for self-study. The level and style of exposition is targeted towards an advanced undergrad or beginning grad student who is into applied math or engineering fields. The authors justly tend to emphasize concepts and applications, instead of getting bogged down in too much mathematical rigor or heavy use of the abstract machinery. All in all, an excellent first excursion/introduction to one of the most fascinating areas of applied math, whether for classroom use, or for self-study.

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Summary: The definitive guide to dynamical systems!
Review: When I purchased this book three years ago, I had only a rudimentary understanding of dynamical systems. Thankfully, all that was needed to get me started was some intermediate calculus and some basic college-level linear algebra. Since I had been doing both from the time I was a sophmore in high school, I had no trouble getting comfortable with it. The authors present dynamical systems in an easy-to-read style with tests that appear at the end of each chapter after you've had time to catch on.

If you're seriously thinking about getting started in dynamical systems, get this book!