In this project the principal investigator will study the structure of waves that arise in a number of physical systems through the action of temporally periodic driving forces. The research will follow two directions. First of all, the principal investigator will study how the effect of temporal driving in exciting the system is balanced by the influence of spatial symmetries. This will entail using some recent methods of bifurcation theory with symmetry to derive and analyze the amplitude equations. Secondly, the principal investigator will study the dynamics of parametrically driven waves in large aspect-ratio systems. Such waves exhibit different types of instabilities that can lead to spatio-temporal chaos. The transitions to this chaotic behavior will be studied analytically as well as numerically.
