Elementary catastrophe theory

This tutorial paper explains some of the basic mathematical ideas involved in René Thom´s Catastrophe Theory, in the simplest and most accessible case: the Elementary Catastrophes. Topics discussed include the classification of local behavior of smooth functions, determinacy (how much of a Taylor series is adequate to capture the function´s behavior), unfoldings (what are the possible perturbations?), and structural stability (robustness). These and other concepts are exemplified using simple models from science: the buckling of an arch, the response of patients suffering from hyperthyroidism to therapy, and cellular differentiation. These models have been selected to act as illustrative examples, and no attempt is made here to survey the applications of the theory since this has already been done in Stewart (1981,1982).