A note on the relation between joint and differential invariants
  We discuss the general properties of the theory of joint invariants of a smooth Lie group action in a manifold. Many of the known results about differential invariants, including Lie's finiteness theorem, have simpler versions in the context of joint invariants. We explore the relation between joint and differential invariants, and we expose a general method that allow to compute differential invariants from joint invariants. 
David Bl\'azquez-Sanz, Juan Sebasti\'an D\'iaz Arboleda
math.DG