Can anything from Noether's theorem be salvaged for discrete dynamical   systems?
  The dynamics of a physical system is linked to its phase-space geometry by Noether's theorem, which holds under standard hypotheses including continuity. Does an analogous theorem hold for discrete systems? As a testbed, we take the Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show that---and why---energy not only acts as a generator of the dynamics for this family of systems, but is also conserved when the dynamics is time-invariant. 
Silvio Capobianco and Tommaso Toffoli
nlin.CG