This research program introduces new methods into the study of dynamical systems and represents a continuation of a program established by the principal investigator. The work is comprised of three major components: (1) Global perturbation methods in dynamical systems related to nonlinear elasticity and fluid mechanics; (2) Studies of knotted period orbits in forced nonlinear oscillators and of the chaotic attracting sets exhibited by such systems; (3) Analysis and predictions of the power spectra of strange attractors and analyses of the effect of small noise on such systems. These studies represent the use of applied mathematics in understanding properties and behavior of mechanical systems.
