The general aim of the satellite is to promote a revitalization of the close relation that has developed between nonlinear dynamical theory and the science of complex systems. It is intended to present recent advances in topics that show contributions towards the understanding of complex systems delivered by the use of nonlinear dynamical concepts. These topics encompass several disciplines: Physics (localization, glass formation), biology (protein folding, circadian rhythms), geophysics (climate, seismicity), ecology (populations evolution, catastrophic extinction), etc. More specifically, we wish to highlight instances in which complex systems described through high-dimensional models experience on certain coarse-grained, macroscopic, scales a considerable reduction of degrees of freedom. This circumstance allows for descriptions based on effective low-dimensional dynamical systems operating in the neighborhood of the onset of chaos. The remarkable collapse of degrees of freedom may turn out to be more general than the few instances in which similar conduct has previously been encountered. It is the purpose of the Satellite to present recent studies of this kind that can become a general guideline for future research in complex systems.