This project is devoted to the study of regular and chaotic motion in nearly integrable infinite dimensional hamiltonian systems. Such systems include certain nonlinear partial differential equations, the wave and vibrating beam equations for instance. Statistical mechanics and condensed matter physics also lead to these systems. The approach consists of extending KAM theory to perturbations of completely integrable hamiltonian systems. Together with the usual methods of the calculus of variation and bifurcation analysis, KAM theory will shed new light on the existence of periodic and quasiperiodic solutions. In addition, geometric and numerical methods will be employed.
