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.

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.