Scientific background and motivation

Dynamical systems are mathematical models that appear in many areas of the natural sciences. They range from simple and classical low-dimensionalmaps and ordinary differential equations to complex networks, partial differential equations, coupled map lattices, delay equations, stochastic differential equations, hybrid systems and many more. Recent years have seen an enormous progress in our understanding of the behaviour of the more complicated and high-dimensionalmodels, ranging from various topological methods to a rush of developments in ergodic theory and random dynamics. Many of these recent developments are happening quickly and much of the theory behind them is technical and hard to access for a relative outsider. It was our belief that scientists working in these different fields of dynamics, including ourselves, are often not keeping up with these developments. We organised this workshop because we thought that researchers in dynamical systems could benefit greatly from a better understanding of each otherís work.



The format of this Lorentz Center workshop was quite experimental: we invited 10 high profile researchers from diverse modernareas of dynamical systems, and asked them to give an extensive introductory lecture on their fields of expertise (each lecture lasted 2 hours). The aim was to give the audience an overview of the important developments and open problems in these fields. We explicitly asked that speakers would not discuss technicalities, but much rather the important questions, leading ideas and crucial insights that have shaped their work and that of others. We also required lecturers to go slowly, to avoid unnecessary details, and to keep their talks understandable.Apart from these key lectures, several PhD students had the opportunity to introduce themselves and their work in a short talk. The program moreover left ample free time for private discussions.



Participants were very positive about the format of this workshop, witness the fact that every lecturer accepted our invitation. Moreover, the Lorentz Center@Snellius is an excellent location for an informal workshop of this kind. Afterwards, we have had many positive reactions from participants about the facilities of the Lorentz Center, the selection, quality and topics of the talks, and theactiveatmosphere during the workshop. Our own impression is that the workshop enabled participants to considerably broaden their horizons. Also, participants made optimal use of the possibility to discuss privately between talks. We estimate the total number of participants of the workshop at 30.



Margaret Beck (Boston, USA)

Jan Bouwe van den Berg (Amsterdam, Netherlands)

Bob Rink (Amsterdam, Netherlands)