The research consists of four parts. In the first, nonlinear dynamical systems with internal resonance is studied for all values of the system parameters so as to get information regarding qualitatively different physical phenomena including chaotic phenomena that can occur in such systems. In the second part, Silnikov theory for four dimensional systems is studied by explicitly computing approximations of the maps. In the third part global phenomena is studied in the case of certain physical systems that tend to develop chaotic behavior. The fourth part consists of a small experimental program in which critical experiments are done as a guide to the theoretical work. This project is largely theoretical but may lead to new insights in the behavior of dynamical systems. Some of the work has a bearing on understanding of forced gravity waves on a fluid surface. Other findings may have relevance to additional engineering issues of immediate concern.
