Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions

by Ralph H. Abraham, Laura Gardini, Christian Mira

Chaos in Discrete Dynamical Systems covers topics in chaos theory, bifurcations and critical curves in a visual, 2-dimensional context. This unique publication is the culmination of a three-year experiment in electronic publishing. As such, it is a package comprised of three carefully intertwined components: a printed book, a cross-platform CD-ROM and a website. The extensively illustrated book is the primary component. The CD-ROM is mainly devoted to presenting 12 computer graphic animations in full color, all tied directly into the content of the book. The user interface to the CD-ROM is made in the style of the world wide web. It is designed to integrate seamlessly with the web site dedicated to this project. This site is maintained by the Visual Math Institute, UC Santa Cruz: http://www.vismath.org/chaos. Motivation for this ambitious package is the conviction that this style of electronic publishing is the ideal medium for mathematical communication. This is especially true for the branch of mathematics known as dynamical systems theory. The essence of this communicative style is the dynapic technique, in which a drawing is developed stroke-by-stroke, along with a carefully coordinated spoken commentary. This is the traditional method used by most mathematicians when speaking among themselves. Visual Math!

Genres: Science

Kindle Edition

First published May 29, 1997

About the author

Dr. Ralph Herman Abraham was a mathematician who specialized in the development of dynamical systems theory. He was a Professor of Mathematics at the University of California, Santa Cruz. He also consulted on chaos theory and its applications in fields such as medical physiology, ecology, mathematical economics, and psychotherapy.

Abraham was also interested in alternative ways of expressing mathematics, for example visually or aurally. He has staged performances in which mathematics, visual arts and music are combined into one presentation. He also developed an interest in "Hip" activities in Santa Cruz in the 1960s and he wrote several books and one website on the topic. He credited his use of psychedelics for inspiring this interest.