NONTRIVIAL COLLECTIVE BEHAVIOR IN EXTENSIVELY-CHAOTIC DYNAMICAL-SYSTEMS - AN UPDATE

Extensively-chaotic dynamical systems often exhibit non-trivial collec tive behavior: spatially averaged quantities evolve in time, even in t he infinite-size, infinite-time limit, in spite of local chaos in spac e and time. After a brief introduction, we give our current thoughts a bout the important problems related to this phenomenon. In particular, we discuss the nature of nontrivial collective behavior and the prope rties of the dynamical phase transitions observed at global bifurcatio n points between two types of collective motion.