The geometry of the elementary catastrophes (1). the cuspoids

Abstract

The Elementary Catastrophes arise as stable singularities in a system of potentials parameterized by a manifold C (the Control Space) on a manifold X (the Behavior Space) and represented by a smooth map: $$V:CxX \to R.$$ The present paper describes the geometry of these singularities for potentials of the type: $$V = \frac{x}{{n + 2}}n + 2 + A\frac{x}{n}n + B\frac{x}{{n - 1}}n - 1 + ... + Rx.$$ and termed the Cuspoids.KeywordsControl SpaceStable SingularityBehavior SpaceCusp CatastropheCommon LimbThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.