Chaos: An Introduction to Dynamical Systems

From the reviews:

“… Written by some prominent contributors to the development of the field … With regard to both style and content, the authors succeed in introducing junior/senior undergraduate students to the dynamics and analytical techniques associated with nonlinear systems, especially those related to chaos … There are several aspects of the book that distinguish it from some other recent contributions in this area … The treatment of discrete systems here maintains a balanced emphasis between one- and two- (or higher-) dimensional problems. This is an important feature since the dynamics for the two cases and methods employed for their analyses may differ significantly. Also, while most other introductory texts concentrate almost exclusively upon discrete mappings, here at least three of the thirteen chapters are devoted to differential equations, including the Poincare-Bendixson theorem. Add to this a discussion of $\omega$-limit sets, including periodic and strange attractors, as well as a chapter on fractals, and the result is one of the most comprehensive texts on the topic that has yet appeared.” Mathematical Reviews