Introduction to Dynamical Systems

ISBN-13: 9780521808415 / Angielski / Twarda / 2002 / 256 str.

College Park) Michael Brin (University of Maryland; College Park) Garrett Stuck (University of Maryland

Opis

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 areas such as number theory, data storage, and internet search engines.

Recenzje

'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

Spis treści

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.