The geometry of the elementary catastrophes: (2). The hyperbolic and elliptic umbilics

Abstract

This paper presents a description of the geometry of the two three-dimensional singularities which are stable with respect to variation of the families of potentials giving rise to them, though not with respect to perturbation directly of the map. They arise from three dimensional families of potentials with domain or "behavior space" at least two dimensional hence their full geometry is essentially five-dimensional.

This work was begun when both authors were at the Institute of Mathematics, University of Warwick, Coventry CV4 7AL Warwickshire, England.