Nonelementary catastrophe theory

Abstract

This tutorial paper is intended to complement the preceding one on Elementary Catastrophe Theory, and to emphasize that many of the supposed limitations of the elementary catastrophes may be overcome by suitably modifying the mathematical setting. The main generalization discussed here is the Imperfect Bifurcation Theory of Golubitsky and Schaeffer Catastrophe Theory with a distinguished parameter. The effects of symmetry are also discussed, leading to some important results on degenerate Hopf bifurcation. Illustrative examples of applications of these ideas are included, but are kept simple to illuminate the mathematical ideas involved. Surveys of applications in the physical sciences of these and related ideas may be found in Stewart (1981, 1982) and in the forthcoming sequel to this tutorial paper. Applications of Non-elementary Catastrophe Theory, to appear in this journal.