A Geometrical Study of the Elementary Catastrophes

The geometry of the elementary catastrophes (1). the cuspoids.- The geometry of the elementary catastrophes: (2). The hyperbolic and elliptic umbilics.- The geometry of the elementary catastrophes: (3). The Parabolic Umbilic.- Stereographic reconstructions of the behaviour space of the cuspoids catastrophes.- Stereographic reconstructions of the catastrophe manifolds of the cuspoids: (2) the swallowtall.- Stereographic reconstructions of the catastrophe manifolds of the cuspoids: (3) the butterfly.- Stereographic reconstuctions of the catastrophe manifolds of the cuspoids: (4) the wigwam.- Stereographic reconstructions of the catastrophe manifolds of the cuspoids: (5) The star.- The geometrical properties of the Reduced Double Cusp.