The spherical phylon group and invariants of the Laplace transform
  We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of $\R^d$ that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform. 
A.L. Carey, M.G. Eastwood, P.E. Jupp and M.K. Murray