Chaos – an introduction to dynamical systems / Kathleen Alligood,. Tim Sauer, James A. Yorke. p. cm. — (Textbooks in mathematical sciences). Request PDF on ResearchGate | Chaos: an introduction to dynamical systems / Kathleen T. Alligood, Tim D. Sauer, James A. Yorke | Incluye bibliografía e. Chaos: An Introduction to Dynamical Systems. Chapter in Physics Cite this publication. Kathleen Alligood at George Mason University. Kathleen Alligood.
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Write a customer review. Showing of 12 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. It was about the mid ‘s, still assimilating the big hype caused by the eventual and much-publicized proof by Andrew Wiles of Fermat’s Last Theorem, when my curiosity bolstered more by having seen a movie such as The Jurassic Park! At that time, the funny, surcastic, and somewhat sloppy foreign professor who happened to be a country-mate of mine, for better or worsehad chosen the brand-new text “Fractals Everywhere” by Michael F.
Barnsely for teaching our mid-size class consisting mainly of senior and first-year graduate students in math and sciences. I recall the discussion starting out by covering the basics about the metric spaces and sequences, and I having a head-start over many others coming fresh on the heels of a heavy-duty general topology course just in the previous semester so for example I could show off to others on the first instruction day what it meant for two metrics to be equivalent.
Still, I admit the semester went by without many of us really absorbing the nuts and bolts of the subject, for example why exactly topological transitivity was needed for chaos in an Iterated Function System, and why exactly some known fractals had the given fractional dimensions eventhough we could compute them.
However the students were generally happy to have scratched the surface of this vast, engaging subject, and for the time being it seemed about enough exposure for most of us. Now looking back, I find Barnsley’s text a very good choice having gone through at the time, but the title by Alligood, Sauer, and Yorke as a recommendation by a college professor at a different school who had taught his students from it seemed like a more well-balanced introduction to the area of dynamical systems.
In fact I also recall at the time there was a discussion as to whether yet another text by Robert Devaney would have made for a better first course. There are 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 undergraduate student who is into applied math or engineering fields. Therefore the authors emphasize concepts and applications instead of getting bogged down in too much mathematical rigor or heavy use of the abstract machinery which is of course needed for a thorough treatment of the subject at an advanced level; there are in fact several newer titles which all occupy this niche.
I needed the book for class. It certainly isn’t the best textbook I’ve used as a math major but it gets the job done.
It could probably use better examples and more clear directives cyaos illustrate points more clearly. I think this book is really strong alligood discrete index dynamical systems Chapters but could use a rewrite on the continuous index portion Chapter 7,8. I haven’t read the later portion. Read this for difference equations, Strogatz for differential equations.
One person found this helpful. This introduce the dynamical systems together with chaos from map and ordinary differentials equations clearly! It also talks about manifold! Very nice introduction to an increasingly important subject. This book is both simple enough to understand, and sophisticated enough to provide further understanding. If you are an second or third year undergraduate planning on graduate work, this book is a great way to catch up on advanced mathematics.
Yorke and his collaborators produced what is probably the best available textbook on chaos. It is meant for both the beginer and the advanced student. This book presents brilliantly the dunamical to Dynamical Systems and Chaos.
CHAOS: An Introduction to Dynamical Systems
Full of exercises, computer experiments and Challenges. I think that the text looses some substance due to the lack of presenting more or all the solutions to the Exercises. They should be solved detailed in a Solutions Manual. Don’t try to e-mail the authors for more solutions, they will not get them to you. This point is the only pitty in a text that is a great companion through chaotic dynamicsl. Also Very Brilliant for me at this Level are: More sofisticated maths but not too far away are: See all 12 reviews.
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Math – Dynamical Systems and Chaos
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CHAOS: An introduction
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