Bibliography of Books on Chaos and Related Topics

The following books will serve as useful outside reading for the serious student.  Most are available in libraries on campus.

Abarbanel, H. D. I., Analysis of Observed Chaotic Data (Springer-Verlag, 1996).  This somewhat mathematical book is probably the most current, detailed, and rigorous treatment of modern chaotic time-series analysis techniques.

Alligood, K. T., Sauer, T. D., and Yorke, J. A., Chaos: An Introduction to Dynamical Systems (Springer, 1996).  This rather standard textbook is aimed at advanced undergraduate and beginning graduate students with a good background in mathematics.  It contains theorems and proofs, computer exercises, and pretty pictures, but very little on time-series analysis.

Bak, P., How Nature Works: The Science of Self-organized Criticality (Springer-Verlag, 1996).  This nonmathematical popularization by the father of the SOC paradigm argues for the generality of such models in explaining a very wide range of natural processes, from sandpiles to human brains.

Baker, G. L. and Gollub, J. P., Chaotic Dynamics: An Introduction (Cambridge Univ. Press, 1996).  This elementary undergraduate text emphasizes chaotic flows in systems described by ordinary differential equations such as the driven pendulum.

Barnsley, M. F., et. al., The Science of Fractal Images (Springer-Verlag, 1988).  This is a very readable collection of articles describing the mathematics that underlies the computer generation of fractal patterns.

Berge, P., Pomeau, Y., and Vidal, C., Order withing Chaos: Towards a Deterministic Approach to Turbulence (John Wiley & Sons, 1986). This very readable book covers the fundamentals of chaos at about the level of this course and includes some practical applications.

Devaney, R. L., A First Course in Chaotic Dynamical Systems: Theory and Experiment (Addison Wesley, 1992).  This undergraduate mathematics book provides an excellent formal introduction to chaos and fractals.  (See also the other books by Devaney.)

Froyland, J., Introduction to Chaos and Coherence (IOP Publishing, 1992).  This is a short mathematical book that goes beyond the level of this course.

Gleick, J., Chaos: Making a New Science (Viking Penguin, 1987).  Everyone should read this best-selling, historical, nontechnical account to understand why people are so excited about chaos.

Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1983).  This is an advanced but standard text that's good for anyone who wants to dig deeper into the mathematics of the topics we are covering.

Gulick, D., Encounters with Chaos (McGraw-Hill, 1992).  Here's a book that has all the theorems and proofs that we are omitting in our course.

Hall, N. (ed.), The New Scientist Guide to Chaos (Penguin, 1992).  This is an excellent summary of the applications, but with little mathematics.

Hilborn, R. C., Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Oxford University Press, 1994).  This book was chosen as our text because of its breadth and depth of coverage.  It emphasizes the computer as a learning tool, and it has a thorough, up-to-date, annotated bibliography.  It contains more material than we will cover and at a higher level, but you will be pleased to have it as a reference.

Jackson, E. A., Perspectives of Nonlinear Dynamics (Cambridge Univ. Press, 1991).  This two-volume graduate-level text is a bit more advanced than our text, but covers all the essentials and includes many nice drawings.

Kaye, B. H., A Random Walk Through Fractal Dimensions (VCH Publishers, 1989).  Here's a book that explains how to characterize fractals produced algorithmically and also those found in nature.

Kranz, H. and Schrieber, T., Nonlinear Time Series Analysis (Cambridge Univ. Press, 1997).  This highly readable book describes most of the modern techniques for analyzing chaotic experimental time series data.  It includes simple computer program listings in FORTRAN and C for most of the common tests.

Lorenz, E. N., The Essence of Chaos (Univ. of Washington Press, 1993).  This series of popular lectures by one of the pioneers in the field attempts (with some success) to explain the mathematical ideas underlying chaos without using equations.

Mandelbrot, B. B., The Fractal Geometry of Nature (Freeman, 1982).  This extended essay by the father of fractals was the seminal work that brought to the attention of the nonspecialist the ubiquity of fractals in nature.  Read it if you're still not sure what fractals have to do with the real world.

Martelli, M., Introduction to Discrete Dynamical Systems and Chaos (Wiley-Interscience, 1999).  This somewhat mathematical text is aimed at upper undergraduate math majors and is limited to discrete dynamical systems.

Moon, F. C., Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers (Wiley, 1992).  Here's a book with more of an engineering flavor that includes many practical applications and examples of chaotic behavior.  It's an update of an earlier (1987) edition.

Nagashima, H., and Baba, Y., Introduction to Chaos (IOP Publishing, 1998).  This is another short mathematical book that goes beyond the level of this course.  It is more difficult than Froyland, but discussion of the logistic map is useful.

Ott, E., Chaos in Dynamical Systems (Cambridge Univ. Press, 1993).  This is a very insightful, graduate level text by one of the most prolific researchers in the field, using high-level mathematics only as necessary to elucidate the concepts and not as an end in itself.

Ott, E., Sauer, T., and Yorke, J. A., Coping With Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems (Wiley, 1994).  This book is very good on time-series analysis and some of the techniques for controlling chaotic systems pioneered by the authors.

Peak, D. and Frame, M., Chaos Under Control (Freeman, 1994).  This book is a text for a course on fractals, chaos, and complexity intended for nonscientists.  It covers a lot of ground especially with fractals using only high school algebra, but it doesn’t go very deeply into the principles of chaos.

Peitgen, H. O. and Richter, P. H., The Beauty of Fractals: Images of Complex Dynamical Systems (Springer-Verlag, 1986).  Here's a book that will boggle your mind with beautiful images mainly from the Mandelbrot and Julia sets.  It's computer art at its finest.  (See also the other books co-authored by Peitgen.)

Pickover, C. A., Computers, Pattern, Chaos and Beauty: Graphics from an Unseen World (St. Martin's Press, 1990).  This is a how-to book by the master of computer graphic art and visualization filled with original ideas for the computer generation of fractals and other artistic patterns.  (See also the many other engaging books by Pickover.)

Ruelle, D., Chance and Chaos (Princeton Univ. Press, 1991).  This charming little book by a pioneer in chaos describes with minimal mathematics the philosophical implications of chaos and randomness.

Schroeder, M., Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise (Freeman, 1991).  This is a highly readable book packed with examples of temporal and spatial chaos in enormously diverse contexts (and a wealth of puns).

Sprott, J. C., Strange Attractors: Creating Patterns in Chaos (M&T Books, 1993).  This is a popularization that uses computer art as a means for discussing the principles of chaos.  It's included here on the strength of its author.

Stewart, I., Does God Play Dice?: The Mathematics of Chaos (Blackwell, 1989).  This is a charming little book that's basically a popularization but that doesn't shy away from using simple mathematics.

Strogatz, S. H., Nonlinear Dynamics and Chaos (Addison Wesley, 1994).  This book might have served as a text for the course except that it has a slightly more mathematical bent, and it doesn't have much on time-series analysis.

Thompson, J. M. T. and Stewart, H. B., Nonlinear Dynamics and Chaos (Wiley, 1986).  This is a standard advanced undergraduate text aimed at physical science students.  It's a bit uneven in the level of treatment of the various topics, but it might have served as a text for our course.

Tong, H., Non-linear Time Series: A Dynamical Systems Approach (Oxford University Press, 1990).  This fairly comprehensive mathematical treatment of time series analysis has many examples of real-world time-series data.

Tsonis, A. A., Chaos: From Theory to Applications (Plenum Press, 1992).  This book is especially good on the time-series analysis topics that are largely missing from the other books.  It might have been a text for our course except that it is less thorough, has fewer references, and costs a bit more than Hilborn.

Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, 1990).  This is a relatively advanced mathematical treatment of the fundamental concepts of nonlinear dynamics and chaos.