Moving Frames and Noether’s Finite Difference Conservation Laws II

In this second part of the paper, we consider finite difference Lagrangians which are invariant under linear and projective actions of SL(2), and the linear equi-affine action which preserves area in the plane.

Effectively, for all three actions, we show that solutions to the Euler–Lagrange equations, in terms of the original dependent variables, share a common structure for the whole set of Lagrangians invariant under each given group action, once the invariants are known as functions on the lattice.