Generic distance-squared mappings on plane curves

Abstract

A distance-squared function is one of the most significant functions in the application of singularity theory to di¤erential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of a given plane curve and generic distance-squared mappings on the plane into the plane are investigated from the viewpoint of stability.