This project spans a variety of fields in ergodic theory. Professor Bergelson will concentrate on the study of multiple recurrence and mixing in dynamical systems. The problems to be researched are closely related to combinatorics and number theory. Professor Rosenblatt research will be in the area of almost everywhere convergence of various averaging methods. This award will also support Dr. Ward, a postdoctoral researcher. His work involves the relationship between positive entropy, mixing of all orders, exponential recurrence, and the action of the integer lattice on compact groups. Because dynamical systems can display extremely complicated, even chaotic behavior, it is impossible to follow the time development of such a system in complete detail. Ergodic theory involves methods of studying certain average properties of these systems which contain enough information to nevertheless be useful.
