Transformations Generalizing the Levi-Civita, Kustaanheimo-Stiefel, and   Fock Transformations
  Preliminary results concerning non-quadratic (and non-bijective) transformations that exibit a degree of parentage with the well known Levi-Civita, Kustaanheimo-Stiefel, and Fock transformations are reported in this article. Some of the new transformations are applied to non-relativistic quantum dynamical systems in two dimensions. 
M. Kibler and P. Labastie