In recent years Dynamical Systems has attracted attention from workers in diverse fields. The use of powerful computers and computer graphics in numerical simulations has led to growing interest in “chaos”. A wide range of scientists including theoretical physicists, engineers, biologists and ecologists have raised interesting problems which provide new sources of “applied” motivation beyond the traditional questions from classical mechanics. Their interaction with mathematicians has stimulated new lines of research and has been particularly important in determining the new directions taken by Dynamical Systems in the last decade.

The approaches to these new problems have several themes in common. Complicated structures are modelled by deterministic systems with a few variables. The bifurcation patterns of parametrized families of systems are studied. Flows are reduced to Poincare maps and all systems are modelled by one-dimensional maps whenever possible. In experimental systems, attractors are reconstructed from time series.

Typical questions of interest are to prove the existence of numerically observed “strange attractors” such as that in the Henon map and to describe the structure of such strange attractors. We would like to understand how these complicated sets can be created from dynamically simple ones through a series of bifurcations. Different kinds of scaling behaviour in strange sets can be found and must be explained. In low dimensional systems the possible range of dynamical behaviour is restricted and so, in principle, should be capable of classification.