This project supports resear5ch in dynamical systems with significant emphasis on computation. The specific projects discussed in the proposal are: 1. Hilbert's 16th Problem: Numerical and symbolic computations to obtain bounds on the number of limit cycles possessed by polynomial vector fields in the plane. 2. Dynamical studies of vector fields derived from equations of fluid boundary layers. 3. The implementation of perturbation methods for ordinary differential equations problems using MACSYMA. 4. The study of multiparameter systems of differential equations near points of multiple bifurcation. 5. Numerical studies of the complex Henon mapping, holomorphic diffeomorphism of complex two space. 6. Symbolic computation of polynomial knot invariants associated to periodic orbits of three dimensional flows. More broadly, the project will support the development of algorithms and efficient computing environments for the studies of dynamical systems.
