Generating functions for volume-preserving transformations

► A general implicit solution for determining volume-preserving transformations in the n-dimensional Euclidean space is obtained. ► For n = 2, it corresponds to the classical definition of a potential stream function in a canonical transformation. ► For n = 3, it defines a more general class of isochoric transformations, if compared to existing methods based on multiple potentials. ► This representation method is suitable for determining three-dimensional isochoric perturbations in bifurcation theory. ► Applications in non-linear elasticity are envisaged for determining complex instability patterns for soft elastic materials.