Complexity and chaos

The papers in this volume summarize the state-of-the-art in the use of concepts of dynamical systems theory to study chaotic evolution and spatiotemporal complexity. The central results of dynamical systems theory have demonstrated that simple deterministic mathematical systems can produce highly disordered dynamical behaviour, suggesting that it might be possible to explain complex natural phenomena with relatively simple models. This proved to be far more difficult than had been initially anticipated. It is increasingly clear that the naive implication of dynamical methods can readily produce spurious indications of deterministic behaviour. Many dynamicists are currently preoccupied with the development of methods that can bring increased rigor and reliability to the analysis of experimental data. At the same time, techniques have been developed for controlling the behaviour of complex systems, for predicting their evolution, and for describing their behaviour even when this behaviour displays complexity in space as well as in time. The papers in this collection discuss techniques used to confirm the existence of chaotic behaviour by means of surrogate data, topological information and quantitative measures of determinism, techniques for controlling and predicting chaotic behaviour, and illustrations of the use of these techniques in laser physics acoustics, hydrodynamics, oceanography, climatology, biology, medicine, and economics.