Kaplan-Yorke attractor (created with Dynamics)
book     Books by the Maryland Chaos Group

C'est une chose extraordinaire que toute la philosophie consiste dans ces trois mots: << je m'en fou. >> - Montesquieu

* Alligood, K.T., Sauer, T., and Yorke, J.A. CHAOS: An Introduction to Dynamical Systems, Springer-Verlag, expected in June of 1996. A review of the book by the American Scientist is available online. Another review from Physics Today is also available. **NOTE**: You also have access to an interesting web page containing Chaos animations.
A very readable introductory text that is designed for students in mathematics and the sciences (undergraduate to beginning graduate level). The book gives a clear and intuitive presentation of the topics and also illustrates the concepts using selected physical experiments in the "Lab Visits" sections. All the important concepts in discrete (iterated maps) and continuous (differential equations) dynamical systems are covered in a careful and detailed manner. Unlike other introductory texts, it does not shy away from presenting deep and important theorems like the Poincaré-Bendixson Theorem, Stable Manifold Theorem, and the Cascade Theorem. In addition to explaining its importance, it delves into the heart of the theorems by looking at the proofs. There is nothing like working through a difficult problem by oneself to get a handle on the concepts, and the "Challenge" sections in the book do just that by letting the reader tackle challenging problems from dynamics. Don't worry, one is guided along the way with many helpful hints. Of course, the importance of chaos would not have been widely appreciated if not for computer simulations, thus the book has "Computer Experiments" sections which guide the reader in exploring the dynamics on computers. Undergraduate Level.

* Helena E. Nusse and James A. Yorke, Dynamics: Numerical Explorations, Second, Revised and Expanded Edition, 608 + xvi pp., Springer-Verlag, New York, 1998.
The book is accompanied by software programs Dynamics 2 and SmallDyn 2, an interactive program for IBM compatible PC's and Unix computers. The Unix version of the program is by Brian R. Hunt and Eric J. Kostelich.

Dynamics runs on MS Windows versions up to "98" and "ME".
SmallDyn runs on MS Windows versions up to "2000"
SmallDyn is a version of Dynamics that has almost all its capabilities.

Dynamics: Numerical Explorations provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in the programs Dynamics and SmallDyn and they should be useful to everyone exploring dynamical systems. Many of the examples reveal patterns that are not fully understood and have surprises lurking just beyond the edges of the imagination.
Dynamics is a toolkit in which the tools are all available at any moment, enabling you to explore the system with much greater ease than if each tool was a separate program. The program iterates maps and solves differential equations. Both programs have an Add-Your-Own-Equations facility.
Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics requires either a Unix workstation running X11 graphics or an IBM PC compatible computer.
See Publications Software for more information.

+ Edward Ott,  Chaos in Dynamical Systems, Second Edition Cambridge University Press, 2002.
An excellent text that is written in a very understandable and careful style. The expanded second edition contains many more homework problems than the previous edition. There is a vast amount of new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange non-chaotic attractors. The book also includes an entirely new chapter on control and synchronization of chaos. The bibliography at the end of the book is also a good source for readers who want to delve further into the technical literature. Graduate Level.

+ Edited by Ott, E., Sauer T., and Yorke, J. A., Coping with Chaos, John Wiley & Sons, 1994.
A more contemporary set of reprints. Very good in practical applications of chaos. Demonstrates how a basic knowledge of chaos theory can be used to evaluate chaotic experimental time series data and how to apply the presence of chaos to achieve practical goals. After familiarizing the reader with fundamental concepts of chaos, the text introduces the important topics of dimension, symbolic dynamics, Lyapunov exponents and entropy. Contains extensive reprints from major papers on the subject and concludes with a research bibliography of articles directed toward coping with chaos. Graduate Level.