Are there Contact Transformations for Discrete Equations?
  We define infinitesimal contact transformations for ordinary difference schemes as transformations that depend on $K+1$ lattice points $(K \geq 1)$ and can be integrated to form a local or global Lie group. We then prove that such contact transformations do not exist. 
Decio Levi, Zora Thomova and Pavel Winternitz
math-ph math.MP