Canonical Forms of 3D Cusp-Fold Singularities and its Unfolding

Key Points

• The study identifies 32 distinct canonical forms for 3D cusp-fold singularities, expanding our understanding of their properties.
• Each canonical form is topologically unique, providing essential insights into the structure of cusp-fold singularities in vector fields.
• Bifurcations of these forms are explored, further detailing the behavior of vector fields near cusp-fold singularities.
• This work highlights the importance of piecewise smooth vector fields in understanding topological aspects of singularities.