Programme leaders: A. Doelman, C.J. van Duijn
The main theme of this programme is the analysis of nonlinear differential equations and dynamical systems, from low dimensional systems such as maps (or discrete systems) and ordinary differential equations, to high dimensional systems, such as partial differential equations and lattice equations. It is the aim of the programme to develop fundamental insight in the complex behavior exhibited by nonlinear systems. The combination and cross-fertilization of mathematical analysis and numerical methods plays an essential role in this context. The character of the scientific research may be of a pure mathematical nature, but can also be mostly numerical. The motivation may be intrinsically mathematical, or can be driven by interactions with applications.
Status of the programme
On the one hand, the mathematical theory of nonlinear systems has developed in an almost explosive fashion in recent years. On the other hand, nonlinear systems are a natural link between mathematics and a growing number of related disciplines, or applications, such as physics, biology, economics, etc. In other words, the field of differential equations, dynamical systems and numerical analysis has a pivotal position, both within mathematics and between mathematics and its applications.
Within this programme, close cooperation exists with research groups in Atlanta, Bath, Bonn, Bordeaux, Boston, Houston, Madrid, Minneapolis, Nottingham, Paris, Parma, Pittsburgh, Providence, Princeton, Sapporo, Tel Aviv, Warwick, etc.