Non-trivial collective behavior in extensively-chaotic dynamical systems: an update

Extensively-chaotic dynamical systems often exhibit non-trivial collective behavior: spatially-averaged quantities evolve in time, even in the infinite-size, infinite-time limit, in spite of local chaos in space and time. After a brief introduction, we give our current thoughts about the important problems related to this phenomenon. In particular, we discuss the nature of non-trivial collective behavior and the properties of the dynamical phase transitions observed at global bifurcation points between two types of collective motion.