Generic Singularities in Elliptic Refractive Systems

In this work, we present a generic classification of a class of n-dimensional piecewise smooth vector fields known as refractive systems. Our purpose is to characterize the local structural stability of refractive fold-folds of elliptic type. To this end, we reduce the study of such piecewise smooth vector fields to the analysis of the first return maps and their structural stability. Normal forms for such systems are also provided.