This project will support a Conference on Dynamical Systems to be held November 1-3, 1989 at the State University of New York at Stony Brook. The conference will bring together experts on dynamical systems and Kleinian groups as well as other mathematicians who work in related areas. The purpose of the meeting is to foster the interaction between the two subdisciplines and to update the "dictionary" (which is essentially an analogy between the theory of iterations of holomorphic and meromorphic maps and the theory of Kleinian groups) between them.