Books by the
Maryland Chaos Group
C'est une chose extraordinaire que toute la philosophie consiste dans
trois mots: << je m'en fou. >>
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
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
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.
Ott, E., Sauer T.,
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.