Gravitational lenses with more than four images. I. Classification of caustics

We study the problem of gravitational lensing by an isothermal elliptical d ensity galaxy in the presence of a tidal perturbation. When the perturbatio n is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextu ple and octuple lenses are likely to be rare because they require special l ens configurations, but a full. calculation of the likelihood will have to include both the existence of lenses with multiple-lens galaxies and the st rong magnification bias that affects sextuple and octuple lenses. At optica l wavelengths, these lenses would probably appear as partial or complete Ei nstein rings, but at radio wavelengths, the individual images could probabl y be resolved.