TABLE OF CONTENTS In this chapter we deal with systems which have bounded solutions for t ? ?, but do not converge to stationary or (quasi-)periodic solutions. In 1 we introduce the concept of sensitive dependence of solutions on the initial conditions. Due to this phenomenon chaotic systems are not predictable in the long run, although they are deterministic. A convenient measure for the sensitivity is provided by the concept of Lyapunov exponents given in 3. In 4 strange and chaotic attractors are considered. There we also discuss why numerically obtained solutions, which unavoidably contain errors, still provide useful information about the properties of these attractors. In 5 the concepts of generalised and fractal dimension are introduced. It is shown that attractors can be characterised by a variety of dimension definitions. Each of these definitions is concerned with a different aspect of the object. The reconstruction of chaotic attractors from experimental data is the subject of 6. The reconstruction technique makes it possible to predict chaotic time series, although within a certain horizon only. The prediction algorithms based on insights from chaos theory are presented in 7.
In Chapter V we analysed solutions remaining bounded for t ? ? and converging to point or periodic attractors. Until fairly recently other types of globally bounded solutions were assumed to be untreatable because of lack of structure. That is why the corresponding systems are usually referred to as being chaotic, but this term is somewhat misleading. Chaos theory is based...
