Topological bifurcation for the double cusp polynomial

Abstract

In his work on elementary catastrophes Zeeman(1) has considered what he has named as the double cusp catastrophe. This catastrophe is defined by the unfolding of the two variable polynomialx4+y4. Using Mather's results (2) on stability of singular germs ofC∞maps we can find an expression for the unfolding. The eight dimensional unfolding can then be considered as a polynomial in two variables with eight parameters.