Multiple bifurcation types and the linear dynamics of ion sputtered surfaces.

We study the patterns formed on ion sputtered Si surfaces as a function of ion energy and incidence angle, and identify a region in parameter space where the flat surface is stable. The boundaries between the stable and pattern-forming regions represent mathematical bifurcations. Our data set exhibits at least two different bifurcation types. We discuss the constraints imposed by these observations on the correct model of long wavelength dynamics of ion sputtered surfaces.