Introduction to Dynamical Systems

A broad introduction, perfect for a one-year graduate course. Includes examples to motivate the theory and some remarkable applications.

Michael Brin (Author), Garrett Stuck (Author)

9780521808415, Cambridge University Press

Hardback, published 14 October 2002

256 pages, 35 b/w illus. 305 exercises
23.6 x 15.9 x 2.2 cm, 0.53 kg

'While the pace is fast and the book is very concise, the organization and selection of topics has been considered carefully, and the writing is strong enough to support the speedy treatment … It certainly does give a notion of the scope of dynamical systems in a way that few other single books do.' Bill Satzer, MAA Reviews

This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

Introduction
1. Examples and basic concepts
2. Topological dynamics
3. Symbolic dynamics
4. Ergodic theory
5. Hyperbolic dynamics
6. Ergodicity of Anosov diffeomorphisms
7. Low-dimensional dynamics
8. Complex dynamics
9. Measure-theoretic entropy
Bibliography
Index.

Subject Areas: Topology [PBP], Geometry [PBM], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ], Mathematics [PB]