Chaos: The Science of Predictable Random Motion

Kautz's [Chaos] functions at the level of Ruelle's [Chance and Chaos] but is more focused and compete. It brings a thorough and fresh approach to the task. The writing is lucid and very engaging ... and the illustrations are uniformly excellent. (James Blackburn, American Journal of Physics)

The book is a famous introduction into the wide field of chaos and provides a very good basis for further studies. It is very useful for many persons: students in engineering, natural sciences, and mathematics or people interested in a better understanding of the nature of chaos. It is highly recommended. (ZAMM - Journal of Applied Mathematics and Mechanics)

Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.