Mathematical Models of Non-Linear Mechanical and Electrical Systems and TheirQualitative Behavior

摘要

Under this grant my students and I conducted research in the following areas. (1)Nonlinear dynamics of coupled and forced oscillators modelling electric circuits; (2) geometric phases in mechanics; (3) two industrial problems, one in fluid dynamics and the other in granular flow; (4) new geometrical results on parametric resonance; (5) Stability and instability of nonlinear Hamiltonian systems, with some applications to geometric optics, using KAM theory. (6) Other research started under this grant is still in progress for 1995.