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.

‘… an ideal choice for a graduate course on dynamical systems … warmly recommended …'

Source: Acta Scientiarum Mathematicarum

‘… exceptionally well written … You should consider adopting this wonderful text for your next graduate course on the pure mathematics of the modern theory of dynamical systems.'

Carmen Chicone Source: SIAM Review

‘… despite the breadth, one finds here major results rigorously treated and substantial applications. By itself, the clean, accessible exposition of the amazing Sharkovsky theorem would justify the acquisition of this book … Highly recommended.'

Source: Choice

‘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 Source: MAA Reviews