Explicit iterative algorithms to reduce a univariate catastrophe to normal form

Abstract

We derive algorithms to solve a technical problem in elementary catastrophe theory: how to reduce an unfolding of a singularity in a univariate function to normal form up to any given degree in the unfolding parameters. Two algorithms that iterate a simple explicit transformation are proposed, which should be suitable for easy implementation using a computer algebra system. They are proved by deriving sufficient vonditions for a class of such algorithms. The complexity and generalization of the algorithms is discussed briefly.