Bunimovich will study mechanisms of space-time chaos and elucidate some convenient and widely used but vague notions of coherent structures, patterns and intermittency. To do this, he will study the behavior of some classes of coupled map lattices that demonstrate most purely these types of motion. He will consider also the related problem of transport in extended systems by investigating the thermodynamic limit of the first examples of systems of arbitrary number of interacting particles recently proven to be ergodic. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way, ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.
