Introduction

This introduction presents an overview of key concepts discussed in the subsequent chapters of this book. The book is an elementary introduction to the theory of dynamical systems and chaos. The principal aim is to explore the deep relationship between dynamical systems, chaos and fractals, and to uncover structure even where order seems to be absent. The approach will combine relatively simple mathematics with computer experiments using the program Chaos for Java, which has been developed specifically for this purpose. Deterministic dynamical systems may exhibit regular behaviour for some values of their control parameters and irregular behaviour for others. One speaks of regular and chaotic behaviour in such a system. In the model from which the Lorenz equations are distilled, the focus of interest is on convective fluid motion driven by heating, such as might occur locally over warm terrain.