THE ANALYSIS OF BIFURCATION SOLUTIONS BY BOUNDARY SINGULARITIES

Abstract

This paper introduces a study of bifurcation of extremals of functions of codimensions eight and twenty four at the origin. We have used the boundary singularities of smooth maps to study the bifurcation analysis of these functions. We have found the parametric equation of the caustic with the geometric description of this caustic. In addition, we have found bifurcation spreading of the critical points by introducing an application on one of our results.