Introducción a la teoría de catástrofes

Abstract

The theory of catastrophes has its origins in Whitney's theory of singularities of which he strongly uses the forms of smooth applications that end up being classified broadly into two types of singularities, fold and cusp. But it was not until the end of the 1950s that the French mathematician René Thom formally introduced the notion of catastrophe for a system with certain characteristics; where he emphasized the fact that they are structurally stable but tend to present discontinuities (abrupt changes in their behavior); that is, a catastrophe is when a perturbation occurs in a stable system. In this monograph we will introduce the notions that allow us to show how these systems can be interpreted by means of soft applications and the classification of these applications, which R. Thom named elementary catastrophes.