Product Description

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

Product Details

• Amazon Sales Rank: #3464323 in Books
• Published on: 2003-06-23
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 436 pages

Review
‘… an excellent presentation of the modern theory of dynamical systems at the advanced undergraduate to intermediate graduate level written by two renowned experts in the field.’ Zentralblatt für Mathematik

‘The book is written in a precise and very readable style, there are many useful remarks and figures throughout. It can be highly recommended to anybody who is interested in dynamical systems and who has a basic knowledge of calculus. The book is also an excellent introduction to the more advanced monograph written by the same authors.‘ European Mathematical Society Newsletter

‘I would recommend that all senior undergraduate physics and engineering students should familiarize themselves with its contents … it is a recommendation for a mathematical perspective on dynamics from an engineer for engineers - and from my discussions with practical physicists a similar recommendation from them.‘ Contemporary Physics

Customer Reviews

An excellent textbook
This is an excellent textbook for anyone who is taking a course in Dynamical Systems, or someone who has read one of the numerous popular maths books on chaos and wants to break into the mathematics of the subject. The course starts fairly gently, but requires an understanding of analysis. Concepts are presented lucidly and includes plenty of exercises, complete with solutions.

The second part of the book introduces modern results, and the famous examples of dynamical systems, such as the Lorenz attractor, Smale's solenoid and homoclinic tangles. The book serves as a good introduction to the modern theory of dynamical systems and leads onto the author's more advanced book, Introduction to the Modern Theory of Dynamical Systems.