This book now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics.
Incorporating numerous new topics and technology not found in similar texts, this book presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems. Written using Mathematica 5.2, the code for the figures and examples in the book is available for download online and is largely compatible with Mathematica 6. Contents
The Stability of One-Dimensional Maps | Attraction and Bifurcation | Chaos in One Dimension | Stability of Two-Dimensional Maps | Bifurcation and Chaos in Two Dimensions | Fractals | The Julia and Mandelbrot Sets Related Topics