The research proposed for this project consists of two sets of questions in the field of dynamical systems and complex analysis. The first set of problems concerns polynomials in a single complex variable. They are an extension of the analysis begun earlier, classifying polynomial dynamic systems in terms of their local behavior near the fixed points. The second set of problems concerns dynamical systems on the 2-torus and the 2-disk. Denjoy- type theorms for homeomorphisms isotopic to the identity on the torus are to be formulated. A computerized method to search for a counterexample to the conjucture that every periodic cycle for every disc homeomorphism is strongly linked with a fixed point is to be outlined on the disk. The investigator is working in the forefront of a very active methematical field--dynamics. The project furthers VPW program objectives to provide opportunities for women to advance their careers in science or engineering through research, and to encourage other women to pursue careers in these areas through the investigators' enhanced visibility as role models on the host campuses. In this project, the proposed activities which contribute to the second objective include: teaching a graduate course entitled Computer Experiments in One-Dimensional Dynamics; and conducting twice-monthly seminars for female graduate and advanced undergraduate students interested in research careers in mathematics, including outside and inside speakers, discussion, and counselling.
