Contact transformations for difference schemes
  We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous limit. We use a simple example to show that the class is not empty and that such "contact transformations for discrete systems" genuinely exist. 
Decio Levi, Zora Thomova and Pavel Winternitz
math-ph math.GR math.MP nlin.SI