Catastrophe Theory

Abstract

Thom’s theory of catastrophes essentially consists of the study of C^∞ families of functions on a manifold, and in particular the variation of their critical points. In the most common applications we are concerned with potentials depending on a finite sequence of control parameters and we study the bifurcation of their equilibrium states. For the reasons given in the Introduction, we are particularly interested in stable families. Moreover, what we want to do essentially is to carry out a local study in the neighbourhood of an equilibrium point and of a given value of the parameters. Specifically, we would like to achieve a classification of the simplest and most common ’catastrophes’.