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A First Course in Dynamics: with a Panorama of Recent Developments
The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.
436 pages, Paperback
First published June 23, 2003
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May 1, 2024
Great overview of various dynamical systems.
Tbh I didn’t do most of the exercise in this book
(perhaps a little above my pay grade as an undergraduate) but there are definitely a lot of them and there were a few here and there I felt comfortable approaching.
I loved the way this book presented new definitions. Instead of just defining a certain property without context, a system was presented and when we came across a new property it was defined rigorously.
The examples in here are fantastic. Lots of info on certain systems and their properties presented in an easy-ish to understand way. Ofc when it comes to dynamical systems it’s good to check what you think will happen numerically for a fuller understanding because some of these properties are pretty hard to grasp just by reading (such as topological mixing, strange attractors, and other things dealing with “almost every point�, denseness, and just generally hard-to-visualize things)
Definitely recommend as a reference for someone dealing with dynamical systems as there are many concise definitions and theorems to cite.
Also recommend to someone who just wants some sort of understanding of dynamical systems without really getting dirty with exercises(this is a rare example of a math book where the reading will actually help you learn without doing every exercise)
Definitely useful for all levels of math students(my professor made a point that this is a book that will stay with you if you study dynamics)
Tbh I didn’t do most of the exercise in this book
(perhaps a little above my pay grade as an undergraduate) but there are definitely a lot of them and there were a few here and there I felt comfortable approaching.
I loved the way this book presented new definitions. Instead of just defining a certain property without context, a system was presented and when we came across a new property it was defined rigorously.
The examples in here are fantastic. Lots of info on certain systems and their properties presented in an easy-ish to understand way. Ofc when it comes to dynamical systems it’s good to check what you think will happen numerically for a fuller understanding because some of these properties are pretty hard to grasp just by reading (such as topological mixing, strange attractors, and other things dealing with “almost every point�, denseness, and just generally hard-to-visualize things)
Definitely recommend as a reference for someone dealing with dynamical systems as there are many concise definitions and theorems to cite.
Also recommend to someone who just wants some sort of understanding of dynamical systems without really getting dirty with exercises(this is a rare example of a math book where the reading will actually help you learn without doing every exercise)
Definitely useful for all levels of math students(my professor made a point that this is a book that will stay with you if you study dynamics)
Displaying 1 of 1 review
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